Section outline

  • Key Concepts

    • The temperature of a gas is a measure of the amount of average kinetic energy that the atoms in the gas possess.
      ::气体的温度是测量气体中的原子拥有的平均动能量。
    • The pressure of a gas is the force the gas exerts on a certain area. For a gas in a container, the amount of pressure is directly related to the number and intensity of atomic collisions on a container wall.
      ::气体的压力是气体对某一区域施加的压力,就容器中的气体而言,压力的程度与集装箱墙上原子碰撞的次数和强度直接相关。
    • An ideal gas is a gas for which interactions between molecules are negligible, and for which the gas atoms or molecules themselves store no potential energy. For an “ideal” gas, the pressure, temperature, and volume are simply related by the ideal gas law.
      ::理想气体是一种分子相互作用可忽略不计的气体,而气体原子或分子本身却不储存潜在的能量。 对于“理想”气体来说,压力、温度和体积只是与理想气体法相关联的。
    • Atmospheric pressure ( Pascals) is the pressure we feel at sea level due to the weight of the atmosphere above us. As we rise in elevation, there is less of an atmosphere to push down on us and thus less pressure.
      ::大气压力(Pascals)是大气在海平面上的压力。 大气压力(Pascals)是我们感到的海平面的压力,因为大气在我们上面的重量。 当我们升起高地时,大气压力就更少了,而压低了。
    • When gas pressure-forces are used to move an object then work is done on the object by the expanding gas. Work can be done on the gas in order to compress it.
      ::当气体压力力用于移动物体时,扩展的气体会对该物体进行工作。可以对气体进行压缩。
    • Adiabatic process: a process that occurs with no heat gain or loss to the system in question.
      ::隔热过程:发生过程时,有关系统不会受到热增益或损失。
    • Isothermal: a process that occurs at constant temperature (i.e. the temperature does not change during the process).
      ::异热:在恒定温度下发生的过程(即温度在过程中不会变化)。
    • Isobaric: a process that occurs at constant pressure.
      ::惰性:一个在持续压力下发生的过程。
    • Isochoric: a process that occurs at constant volume.
      ::学说:一个在恒定体积时发生的过程。
    • If you plot pressure on the vertical axis and volume on the horizontal axis, the work done in any complete cycle is the area enclosed by the graph. For a partial process, work is the area underneath the curve, or.
      ::如果您在水平轴上绘制垂直轴和体积的压力图,则在任何完整循环中完成的工作是图中附加的区域。对于部分过程,工作是曲线下的区域,或。
    • In a practical heat engine, the change in internal energy must be zero over a complete cycle. Therefore, over a complete cycle .
      ::在一个实用的热力引擎中,内部能量的改变必须在整个周期内为零。 因此,在一个完整周期内为零。
    • The work done by a gas during a portion of a cycle = , note can be positive or negative.
      ::气体在某一周期的某一部分中完成的工作 =,注可以是正的,也可以是负的。
    • The efficiency of any heat engine :
      ::任何热引擎的效率:
    • An ideal engine, the most efficient theoretically possible, is called a Carnot Engine. Its efficiency is given by the following formula, where the temperatures are, respectively, the temperature of the exhaust environment and the temperature of the heat input, in Kelvins. In a Carnot engine heat is input and exhausted in isothermal cycles, and the efficiency is .
      ::一种理想的引擎,在理论上尽可能有效,叫做卡诺引擎。它的效率来自以下公式,那里的温度分别是开尔文斯排气环境的温度和热输入的温度。在卡诺发动机的热在异热循环中投入和耗尽,效率是。
    • The Stirling engine is a real life heat engine that has a cycle similar to the theoretical Carnot cycle. The Stirling engine is very efficient (especially when compared to a gasoline engine) and could become an important player in today's world where green energy and efficiency will reign supreme.
      ::斯特林引擎是一个真实的生命热力引擎,其周期与理论的卡诺周期相似。 斯特林引擎非常高效(尤其是与汽油引擎相比 ) , 并可能成为当今绿色能源和效率将占据至高无上地位的重要角色。

    Key Equations

    ; the heat gained or lost is equal to the mass of the object multiplied by its specific heat multiplied by the change of its temperature.
    ::;获得或失去的热量等于物体的质量乘以其特定热量乘以其温度的变化。

    ; the heat lost or gained by a substance due to a change in phase is equal to the mass of the substance multiplied by the latent heat of vaporization/fusion ( refers to the latent heat)
    ::;物质因相位变化而损耗或获得的热量等于物质乘以蒸发/聚变潜在热量(指潜在热量)的重量。

    1 cal = 4.184 Joules; your food calorie is actually a kilocalorie (Cal) and equal to 4184 J.
    ::1口径=4.184焦耳;你的食物卡路里实际上是一个千卡路里(Cal),等于4184焦耳。

    is the internal energy of the gas. (This is the first law of Thermodynamics and applies to all heat engines.)
    ::是气体的内部能量。 (这是热力学的第一定律,适用于所有热引擎。 )

    The average kinetic energy of atoms (each of mass and average speed ) in a gas is related to the temperature of the gas, measured in Kelvin. The Boltzmann constant is a constant of nature, equal to .
    ::气体中原子的平均动能(质量和平均速度)与用克尔文测量的气体温度有关。波尔茨曼常数是自然常数,等于 。

    The pressure on an object is equal to the force pushing on the object divided by the area over which the force is exerted. Unit for pressure are (called Pascals)
    ::对物体的压力等于对物体的推力,推力按所施力的面积分隔。 压力单位为( 称为 Pascals ) 。

    An ideal gas is a gas where the atoms are treated as point-particles and assumed to never collide or interact with each other. If you have molecules of such a gas at temperature and volume , the pressure can be calculated from this formula. Note that ; this is the ideal gas law
    ::理想气体是一种气体,其中原子被当作点粒子处理,并假定它们从不相撞或相互作用。如果在温度和体积上有这种气体的分子,那么压力可以从这个公式中计算出来。请注意,这是理想气体法。请注意,这是理想气体法。

    is the volume, is the number of moles; is the universal gas constant ; this is the most useful form of the gas law for thermodynamics.
    ::是体积,是摩尔数;是通用气体常数;这是热力学气体法最有用的形式。

    where and are the temperatures of the hot and cold reservoirs, respectively.
    ::热水库的温度和冷水库的温度是分别的。

    Molecular Kinetic Theory of a Monatomic Ideal Gas

    The empirical combined gas law is simply a generalization of observed relationships. Using kinetic theory, it is possible to derive it from the principles of Newtonian mechanics. Previously, we thought of an ideal gas as one that obeys the combined gas law exactly. Within the current model, however, we can give a specific definition. We treat a monatomic ideal gas as a system of an extremely large number of very small particles in random motion that collide elastically between themselves and the walls of their container, where there are no interaction between particles other than collisions.
    ::实证合并天然气法只是对观察到的关系的一种概括。 使用动能理论,它有可能从牛顿力学原理中产生。 以前,我们把理想气体视为完全遵循联合天然气法的气体。 但是,在目前的模型中,我们可以给出一个具体的定义。 我们把一个单质理想气体视为一个由数量极小的微粒随机运动组成的系统,在它们自己和容器的墙壁之间发生碰撞,在其中,除了碰撞之外,粒子之间没有相互作用。

    Consider some amount ( atoms) of such a gas in a cubical container with side length . Let's trace the path of a single gas atom as it collides with the walls:
    ::将这种气体在侧长的隔间容器中的某些数量(原子)考虑进去。

    Ideal Gas Theory

    The path of a single gas atom as it undergoes collisions with the walls of its container
    ::单一气体原子与其容器墙壁碰撞时的路径

    Further, let's restrict ourselves to considering the motion of the particle along the axis, and its collisions with the right wall, as shown in the picture. Therefore, we only consider the component of the velocity vector perpendicular to the wall.
    ::此外,我们只考虑粒子沿着轴的移动, 以及它与右墙的碰撞,正如图片所示。 因此,我们只考虑与墙垂直的高速矢量的成分。

    If the particle's mass is , in one collision, the particle's momentum in the direction changes by
    ::如果粒子的质量在一次碰撞中 粒子向方向的动力变化

    Also, since it has to travel a distance (back and forth, basically) in the direction between collisions with the right wall, the time between collisions will be
    ::此外,由于它必须从与右墙相撞的距离(基本上前后)向右墙相撞的方向移动,碰撞的时间将是:

    Ideal Gas Theory 2

    Illustration x-direction atom from above.
    ::说明 X - 方向原子来自上方。

    According to Newton's second law, the force imparted by the single particle on the wall is
    ::根据牛顿的第二项法律 墙上的单粒子所传递的力量是

    Now, since there are (a very large number) atoms present, the net force imparted on the wall will be
    ::现在,由于目前存在原子(数量很大),隔离墙上的净力量将是:

    Where the is averaged over all atoms.
    ::在所有原子中都是平均的。

    Now let us attempt to relate this to the state variables we considered last chapter. Recall that pressure is defined as force per unit area:
    ::现在让我们尝试将这一点与我们最后一章考虑的状态变量联系起来。 回顾压力被定义为单位面积的强度:

    Since the area of the wall in question is , the pressure exerted by the gas atoms on it will equal:
    ::由于有关墙的面积是......,气原子对墙上的压力将等于:

    Since, for a cubical box, volume , the formula above can be reduced to:
    ::由于对立方体体体积而言,上述公式可减至:

    By the Pythagorean theorem, any three-dimensional velocity vector has the following property:
    ::根据毕达哥里定理,任何三维速度矢量具有以下属性:

    Averaging this for the particles in the box, we get
    ::把这个换成盒子中的粒子 我们得到

    Since the motions of the particles are completely random (as stated in our assumptions), it follows that the averages of the squares of the velocity components should be equal: there is no reason the gas particles would prefer to travel in the direction over any other. In other words,
    ::由于粒子的移动是完全随机的(正如我们在假设中所说),因此速度元件平方的平均值应当相等:气体粒子没有理由偏向于其他任何方向。换句话说,

    Plugging this into the average equation above, we find:
    ::将它融入以上平均方程式中,我们发现:

    Plugging this into equation [1], we get:
    ::把这个插进方程[1],我们得到:

    The left side of the equation should look familiar; this quantity is proportional to the average kinetic energy of the molecules in the gas, since
    ::方程的左侧应该看起来很熟悉;这个数量与气体中分子的平均动能成正比,因为

    Therefore, we have:
    ::因此,我们:

    This is a very important result in kinetic theory, since it expresses the product of two state variables , or system parameters, pressure and volume, in terms of an average over the microscopic constituents of the system. Recall the empirical ideal gas law from last chapter:
    ::这是动能理论的一个非常重要的结果,因为它代表了两种状态变量的产物,或系统参数、压力和体积,即系统微生物成分的平均值。 回顾上一章的经验理想气体法:

    The left side of this is identical to the left side of equation [3], whereas the only variable on the right side is temperature. By setting the left sides equal, we find:
    ::此方程的左侧与方程的左侧相同[3],而右侧唯一的变量是温度。通过将左侧设为等值,我们发现:

    Therefore, according to the kinetic theory of an monoatomic ideal gas, the quantity we called temperature is --- up to a constant coefficient --- a direct measure of the average kinetic energy of the atoms in the gas . This definition of temperature is much more specific and it is based essentially on Newtonian mechanics.
    ::因此,根据单原子理想气体的动能理论, 我们称之为温度的数量 -- 最高为恒定系数 -- 直接测量气体中原子的平均动能。 温度的定义要具体得多, 基本上以牛顿力学为基础。

    Temperature, Again
    ::温度, 再次

    Now that we have defined temperature for a monoatomic gas, a relevant question is: can we extend this definition to other substances? It turns out that yes, we can, but with a significant caveat. In fact, according to classical kinetic theory, temperature is always proportional to the average kinetic energy of molecules in a substance. The constant of proportionality, however, is not always the same.
    ::现在,我们已经定义了单原子气体的温度,一个相关的问题是:我们能否将这一定义扩大到其他物质呢?事实证明,我们可以,但有一个重要的警告。 事实上,根据传统的动能理论,温度总是与物质中分子的平均动能成比例的。 然而,相称性的常数并不总是一样。

    Consider: the only way to increase the kinetic energies of the atoms in a monoatomic gas is to increase their translational velocities. Accordingly, we assumed above that the kinetic energies of such atoms are stored equally in the three components () of their velocities.
    ::考虑一下:在单原子气体中增加原子动能的唯一方法就是增加其翻译速度。 因此,我们在上面假设这些原子的动能同样储存在其速度的三个()组成部分中。

    On the other hand, diatomic gases consist of two atoms connected by a bond. The two atoms and bond can be modeled as a spring or a harmonic oscillator. Now, a single molecule's kinetic energy can be increased either by increasing its speed, by making it vibrate in simple harmonic motion, or by making it rotate around its center of mass . This difference is understood in physics through the concept of degrees of freedom : each degree of freedom for a molecule or particle corresponds to a possibility of increasing its kinetic energy independently of the kinetic energy in other degrees.
    ::另一方面,二原子气体由两个原子组成,两个原子通过连接连接。两个原子和连接可以模拟为弹簧或感应振动器。现在,单分子的动能可以通过加快速度、在简单的声波中进行振动或通过在质量中心旋转来增加。在物理学中,通过自由度概念来理解这一差异:分子或粒子的每种自由度都相当于其运动能量增加的可能性,而其他程度的动能不受动能影响。

    It might seem to you that monatomic gases should have one degree of freedom: their velocity. They have three because their velocity can be altered in one of three mutually perpendicular directions without changing the kinetic energy in other two --- just like a centripetal force does not change the kinetic energy of an object, since it is always perpendicular to its velocity. These are called translational degrees of freedom.
    ::在你们看来,单质气体应该有一个自由度:速度。它们有三个, 因为它们的速度可以在三个相互垂直的方向中改变一个, 而不改变其他两个方向的动能-- 就像一个子宫的力不会改变一个物体的动能, 因为它总是与它的速度紧密相连。这些都叫做翻译自由度。

    Diatomic gas molecules, on the other hand have more: the three translational degrees explained above still exist, but there are now also vibrational and rotational degrees of freedom. Monatomic and diatomic degrees of freedom can be illustrated like this:
    ::另一方面,diatomic气体分子则更多:上文解释的三个翻译学位仍然存在,但现在也有振动和旋转的自由度。 分子和二亚原子的自由度可以这样说明:

    Temperature is an average of kinetic energy over degrees of freedom, not a sum . Let's try to understand why this is in reference to our monoatomic ideal gas. In the derivation above, volume was constant; so, temperature was essentially proportional to pressure, which in turn was proportional to the kinetic energy due to translational motion of the molecules. If the molecules had been able to rotate as well as move around the box, they could have had the same kinetic energy with slower translational velocities, and, therefore, lower temperature. In other words, in that case, or assumption that the kinetic energy of the atoms only depends on their velocities, implied between equations [2] and [3], would not have held . Therefore, the number of degrees of freedom in a substance determines the proportionality between molecular kinetic energy and temperature: the more degrees of freedom, the more difficult it will be to raise its temperature with a given energy input.
    ::温度是自由度的动能平均值, 不是总量。 让我们试着理解为什么这与我们的单原子理想气体有关。 在上文的推断中, 体积是恒定的; 因此, 温度基本上与压力成正比, 而这反过来又与分子的翻译运动的动能成正比。 如果分子能够旋转和移动到盒子周围, 它们本可以拥有同样的动能, 翻译速度较慢, 因此温度较低。 换句话说, 换句话说, 换句话说, 假设原子的动能仅取决于方程[ 2] 和 [ 3] 之间所隐含的其速度。 因此, 物质的自由度决定分子动能和温度的相称性: 自由度越高, 越难用给定的能量输入提高温度。

    In solids, degrees of freedom are usually entirely vibrational; in liquids, the situation becomes more complicated. We will not attempt to derive results about these substances, however.
    ::在固体中,自由度通常完全是振动性的;在液体中,情况变得更加复杂。 但是,我们不会试图对这些物质产生结果。

    A note about the above discussion: since the objects at the basis of our understanding of thermodynamics are atoms and molecules, quantum effects can make certain degrees of freedom inaccessible at specific temperature ranges. Unlike most cases in your current physics class, where these can be ignored, in this case, quantum effects can make an appreciable difference. For instance, the vibrational degrees of freedom of diatomic gas molecules discussed above are, for many gases, inaccessible in very common conditions, although we do not have the means to explain this within our theory. In fact, this was one of the first major failures of classical physics that ushered in the revolutionary discoveries of the early 20th century.
    ::关于上述讨论的注解:由于以我们对热力学的理解为基础的物体是原子和分子,量子效应可以使特定温度范围内某些程度的自由无法进入。与目前物理学类中大多数情况不同的是,在这种情况下,量子效应可以忽略,可以产生明显不同。例如,上文讨论的二原子气分子自由的振动度在许多气体非常常见的条件下是无法进入的,尽管我们没有办法在理论中解释这一点。事实上,这是20世纪初革命性发现带来的古典物理学的最初重大失败之一。

    Thermal Energy
    ::热热能

    In light of the above derivation, it should not surprise you that the kinetic energy from motion of molecules contributes to what is called the thermal energy of a substance. This type of energy is called sensible energy . In ideal gases, this is the only kind of thermal energy present.
    ::根据上述推论,分子运动的动能有助于一种物质所谓的热能,这不应令你感到惊讶。这种能量被称为明智的能量。在理想的气体中,这是唯一一种热能。

    Solids and liquids also have a different type of thermal energy as well, called Latent Energy , which is associated with potential energy of their intermolecular bonds in that specific phase --- for example the energy it takes to break the bonds between water molecules in melting ice (remember, we assumed molecules do not interact in the ideal gas approximation).
    ::固体和液体也有不同种类的热能,称为低温能源,这与它们在这一特定阶段的分子内联结的潜在能量有关 -- -- 例如,打破融化冰中的水分子之间的联结所需的能量(记住,我们假定分子在理想的气体近似中不会相互作用)。

    To recap, there are two types of Thermal Energy :
    ::概括地说,热能有两种类型:

    • The kinetic energy from the random motion of the molecules or atoms of the substance, called Sensible Energy
      ::物质分子或原子的随机运动产生的动能能量,称为感官能量
    • The intermolecular potential energy associated with changes in the phase of a system (called Latent Energy ).
      ::与系统阶段变化有关的分子潜能间隙能量(称为低温能源)。

    Heat
    ::热热热

    The term heat is formally defined as a transfer of thermal energy between substances. Note that heat is not the same as thermal energy . Before the concept of thermal energy, physicists sometimes referred to the 'heat energy' of a substance, that is, the energy it received from actual 'heating' (heating here can be understood as it is defined above, though for these early physicists and chemists it was a more 'common sense' idea of heating: think beaker over Bunsen burner). The idea was then to try to explain thermodynamic phenomena through this concept.
    ::热一词被正式定义为物质之间的热能转移。 注意热与热能不同。 在热能概念之前, 物理学家有时会提到一种物质的“热能 ” , 即它从实际的“热”中得到的能量( 这里热能可以理解为上面所定义的, 虽然对于这些早期的物理学家和化学家来说, 热能是一种更“ 常识”的热力概念: 想象Bunsen燃烧器的燃烧器。 那时的想法是试图通过这个概念来解释热力现象。

    The problem with this approach is that thermal energy is the most fundamental to the science, and 'heating' is not the only way to change the thermal energy of a substance . For example, if you rub your palms together, you increase the thermal energy of both palms.
    ::这种方法的问题是热能对科学来说是最基本的,“热能”并不是改变物质热能的唯一方法。 比如,如果你一起擦擦手掌,就会增加两种棕榈的热能。

    Once heat (a transfer of thermal energy) is absorbed by a substance, it becomes indistinguishable from the thermal energy already present: what methods achieved that level of thermal energy is no longer relevant. In other words, 'to heat' is a well defined concept as a verb: its use automatically implies some kind of transfer. When heat using as a noun, one needs to be realize that it must refer to this transfer also, not something that can exist independently.
    ::一旦热能(热能的转移)被一种物质吸收,它就会变得与已经存在的热能无法区分:什么方法实现了热能水平不再相关。 换句话说,“ 热能”是一个定义明确的动词概念:热能的使用自动意味着某种转移。 当热作为名词使用时,人们需要认识到它也必须提到这种转移,而不是独立存在的东西。

    Specific Heat Capacity and Specific Latent Heat
    ::特定热能容量和特定热量

    The ideas in the paragraphs above can be understood better through the concept of specific heat capacity (or specific heat for short), which relates an increase in temperature of some mass of a substance to the amount of heat required to achieve it. In other words, for any substance, it relates thermal energy transfers to changes in temperature. It has units of Joules per kilogram Kelvin. Here is how we can define and apply specific heat ( refers to heat supplied, to the mass of the substance and to its specific heat capacity):
    ::以上各段的想法可以通过特定热容量(或短热特定热量)的概念得到更好的理解,这一概念将某种物质的某些质量的温度上升与达到这一容量所需的热量联系起来,换言之,对任何物质而言,热能转移与温度变化有关,每公斤开尔文有焦耳斯单位。 这就是我们如何定义和应用特定热量(是指提供的热量、物质的质量及其特定热量):

    Heat capacity is largely determined by the number of degrees of freedom of the molecules in a substance (why?). However, it also depends on other parameters, such as pressure. Therefore, the formula above implicitly assumes that these external parameters are held constant (otherwise we wouldn't know if we're measuring a change in specific heat is real or due to a change in pressure).
    ::热容量在很大程度上取决于物质中分子的自由度(原因为何? ) 。 但是,它也取决于其他参数,例如压力。 因此,上面的公式暗含假设这些外部参数保持不变( 否则我们不知道我们衡量特定热量的变化是真实的还是由于压力的变化)。

    When a substance undergoes a phase change, its temperature does not change as it absorbs heat. We referred to this as an increase or decrease in latent energy earlier. In this case, the relevant question is how much heat energy does it require to change a unit mass of the substance from one phase to another? This ratio is known as latent heat , and is related to heat by the following equation ( refers to the latent heat):
    ::当物质发生阶段变化时,其吸收热量的温度不会变化。 我们早先将此称为潜在能量的增减。 在此情况下, 相关的问题是将物质单位质量从一个阶段改变为另一个阶段需要多少热能? 这个比例被称为潜在热量, 并且与热有关, 以下方程( 指潜在热量 ) :

    During a phase change, the number of degrees of freedom changes, and so does the specific heat capacity. Heat capacity can also depend on temperature within a given phase, but many substances, under constant pressure, exhibit a constant specific heat over a wide range of temperatures. For instance, look at the graph of temperature vs heat input for a mole ( molecules) of water at . Note that the x-axis of the graph is called 'relative heat energy' because it takes a mole of water at 0 degrees Celsius as the reference point.
    ::在一个阶段变化期间,自由度变化的数量,以及特定热容量。热能也可以取决于特定阶段的温度,但许多物质,在持续压力下,在一系列广泛的温度中表现出恒定的特定热量。例如,看看温度图和热输入量图,用于水的摩尔(分子)。请注意,该图的x轴被称为“相对热能”,因为它以0摄氏度的水摩尔作为参照点。

    The sloped segments on the graph represent increases in temperature. These are governed by equation [1]. The flat segments represent phase transitions, governed by equation [2]. Notice that the sloped segments have constant, though different, slopes. According to equation [1], the heat capacity at any particular phase would be the slope of the segment that corresponds to that phase on the graph. The fact that the slopes are constant means that, within a particular phase, the heat capacity does not change significantly as a function of temperature.
    ::图形中的斜坡段代表温度的增加。这些由方程式[1]管理。平板段代表阶段过渡,由方程式[2]管理。注意斜坡段具有恒定的,尽管不同的斜坡。根据方程式[1],任何特定阶段的热能力都是与图中该阶段相对应的部分的斜坡。斜坡是恒定的,这意味着在特定阶段中,热能力不会因温度的函数而发生重大变化。

    Table of Specific Heat Values
    Substance Specific Heat,
    Air 6.96
    Water 1.00
    Alcohol 0.580
    Steam 0.497
    Ice 0.490
    Aluminum 0.215
    Zinc 0.0925
    Brass 0.0907
    Silver 0.0558
    Lead 0.0306
    Gold Lead 0.0301
    Table of Heat of Vaporization
    Substance Fusion, Vaporization,
    Water 80.0 540
    Alcohol 26 210
    Silver 25 556
    Zinc 24 423
    Gold 15 407
    Helium - 5.0

    Entropy
    ::信孔号

    The last major concept we are going to introduce in this chapter is entropy. We noted earlier that temperature is determined not just by how much thermal energy is present in a substance, but also how it can be distributed. Substances whose molecules have more degrees of freedom will generally require more thermal energy for an equal temperature increase than those whose molecules have fewer degrees of freedom.
    ::我们将在本章中引入的最后一个主要概念是引温。 我们早些时候曾指出,温度的确定不仅取决于物质中有多少热能,还取决于它是如何分布的。 分子自由度较高的物质一般需要比分子自由度较低的物质更高的热能,以达到同样的温度增长。

    Entropy is very much related to this idea: it quantifies how the energy actually is distributed among the degrees of freedom available. In other words, it is a measure of disorder in a system. An example may illustrate this point. Consider a monatomic gas with atoms (for any appreciable amount of gas, this number will be astronomical). It has degrees of freedom. For any given value of thermal energy, there is a plethora of ways to distribute the energy among these. At one extreme, it could all be concentrated in the kinetic energy of a single atom. On the other, it could be distributed among them all. According to the discussion so far, these systems would have the same temperature and thermal energy. Clearly, they are not identical, however. This difference is quantified by entropy: the more evenly distributed the energy, the higher the entropy of the system. Here is an illustration:
    ::Entropy 与这个概念非常相关: 它量化了能量是如何在可自由度之间实际分配的。 换句话说, 它是一个系统中的混乱度量。 举例来说, 它可以说明这一点。 考虑一种原子的元体气体( 对于任何相当数量的气体, 这个数字将是天文) 。 它有一定程度的自由度。 对于任何给定的热能值, 都有在其中分配能量的多种方法。 在一个极端, 它可能全部集中在一个原子的动能中。 而在另一个极端, 它可以全部分布在其中。 根据目前的讨论, 这些系统具有相同的温度和热能。 但是, 很明显, 它们并不相同。 这个差异是用 entropy 来量化的: 能量分配得更均匀, 系统中的能量越高。 以下为示例: :

    The Laws of Thermodynamics

    Now that we have defined the terms that are important for an understanding of thermodynamics, we can state the laws that govern relevant behavior. These laws, unlike Newton's Laws or Gravity, are not based on new empirical observations: they can be derived based on statistics and known principles, such as conservation of energy. By understanding the laws of thermodynamics we can analyze heat engines , or machines that use heat energy to perform mechanical work.
    ::现在,我们已经定义了对于理解热动力学十分重要的术语,我们可以说明规范相关行为的法律。 与牛顿的法律或重力不同,这些法律并非基于新的经验观察:它们可以基于统计数据和已知原则,如节能。通过理解热动力学的规律,我们可以分析热引擎,或者使用热能进行机械工作的机器。

    The First Law
    ::第一法(第一法)

    The First Law of Thermodynamics is simply a statement of energy conservation applied to thermodynamics systems: the change in the internal --- for our purposes, this is the same as thermal --- energy (denoted ) of a closed system is equal to the difference of net input heat and performed work . In other words,
    ::《热力学第一定律》只是一份适用于热力学系统的节能说明:就我们的目的而言,封闭系统的内部变化与热能(注)相同,相当于净输入热量与实际工作之间的差别。换句话说,

    Note that this does not explain how the system will transform input heat to work, it simply enforces the energy balance.
    ::请注意,这并不解释系统如何将输入热转换成工作,而只是加强能源平衡。

    The Second Law
    ::《第二法》

    The Second Law of Thermodynamics states that the entropy of an isolated system will always increase until it reaches some maximum value . Consider it in light of the simplified example in the entropy section: if we allow the low entropy system to evolve, it seems intuitive collisions will eventually somehow distribute the kinetic energy among the atoms.
    ::热力学第二定律指出,一个孤立系统的酶在达到某种最大值之前总是会增加。 参照一个简化的例子来看待它: 如果我们允许低的酶系统演变, 它似乎直觉的碰撞最终会以某种方式在原子之间分配动能。

    The Second Law generalizes this intuition to all closed thermodynamic systems. It is based on the idea that in a closed system, energy will be randomly exchanged among constituent particles --- like in the simple example above --- until the distribution reaches some equilibrium (again, in any macroscopic system there will be an enormous number of atoms, degrees of freedom, etc). Since energy is conserved in closed systems, this equilibrium has to preserve the original energy total. In this equilibrium, the Second Law --- fundamentally a probabilistic statement --- posits that the energy will be distributed in the most likely way possible. This typically means that energy will be distributed evenly across degrees of freedom.
    ::第二法则将这种直觉概括于所有封闭的热动力系统。它基于这样一种想法:在封闭的系统中,能量将在组成粒子之间随机交换 -- -- 象上文的简单例子一样 -- -- 直到分配达到某种平衡(在任何宏观系统中,同样会有大量原子、自由度等)。由于能源在封闭的系统中被保存,这种平衡必须保持原有的能量总量。在这个平衡中,第二法则 -- -- 从根本上说 -- -- 一种概率说明 -- -- 假设能量将尽可能以最可能的方式分配。这通常意味着能量将平均地分布在自由度之间。

    This allows us to formulate the Second Law in another manner , specifically: heat will flow spontaneously from a high temperature region to a low temperature region, but not the other way . This is just applying the thermodynamic vocabulary to the logic of the above paragraph: in fact, this is the reason for the given definition of temperature. When two substances are put in thermal contact (that is, they can exchange thermal energy), heat will flow from the system at the higher temperature (because it has more energy in its degrees of freedom) to the system with lower temperature until their temperatures are the same.
    ::这使我们能够以另一种方式制定第二法则,具体地说:热量会自发地从高温区域流向低温区域,而不是相反的方式。这仅仅是将热力学词汇应用于上一段的逻辑:事实上,这是给定温度定义的原因。当两种物质被置于热接触状态(即它们可以交换热能)时,温度会从系统高温(因为它的自由度较高)流向温度较低的系统,直到温度相同为止。

    When a single system is out equilibrium, there will be a net transfer of energy from one part of it to another. In equilibrium, energy is still exchanged among the atoms or molecules, but not on a system-wide scale. Therefore, entropy places a limit on how much work a system can perform: the higher the entropy, the more even the distribution of energy, the less energy available for transfer.
    ::当单一系统失去平衡时,就会出现能源从一个部分向另一个部分的净转移。 在平衡中,能源仍然在原子或分子之间交换,但并不是在全系统范围内。 因此,通缩对系统能完成多少工作施加了限制: 信封越高,能源分配越均衡,可用于转移的能源就越少。

    Heat Engines

    Heat engines transform input heat into work in accordance with the laws of thermodynamics. For instance, as we learned in the previous chapter, increasing the temperature of a gas at constant volume will increase its pressure. This pressure can be transformed into a force that moves a piston.
    ::热引擎根据热动力学的定律将输入热转化为工作。例如,正如我们在前一章中学到的, 气体温度的不断升高会增加其压力。这种压力可以转化为一种动活塞的力量。

    The mechanics of various heat engines differ but their fundamentals are quite similar and involve the following steps:
    ::各种热力发动机的机理各不相同,但其基本原理相当相似,涉及以下步骤:

    1. Heat is supplied to the engine from some source at a higher temperature .
      ::热量由某种来源以较高温度供应发动机。
    2. Some of this heat is transferred into mechanical energy through work done .
      ::部分热量通过完成的工程转化为机械能源。
    3. The rest of the input heat is transferred to some source at a lower temperature until the system is in its original state.
      ::输入热的其余部分以较低的温度转移到某些来源,直到系统达到原来的状态。

    A single cycle of such an engine can be illustrated as follows:
    ::这种发动机的单一周期可以说明如下:

    In effect, such an engine allows us to 'siphon off' part of the heat flow between the heat source and the heat sink. The efficiency of such an engine is defined as the ratio of net work performed to input heat; this is the fraction of heat energy converted to mechanical energy by the engine:
    ::实际上,这样的引擎能让我们“吸收”热源和热汇之间部分热流的“吸收”部分。这种引擎的效率被定义为对输入热的纯工作比;这是发动机将热能转换成机械能源的一小部分:

    If the engine does not lose energy to its surroundings (of course, all real engines do), then this efficiency can be rewritten as
    ::如果发动机周围环境不会失去能源(当然,所有真正的引擎都这样做),那么这种效率可以按以下方式改写:

    A Carnot Engine , the most efficient heat engine possible, has an efficiency equal to
    ::Acronot 引擎, 尽可能最有效的热发动机, 其效率相当于

    where and are the temperatures of the hot and cold reservoirs, respectively.
    ::热水库的温度和冷水库的温度是分别的。

    Some Important Points
    ::一些重要要点

    • In a practical heat engine, the change in internal energy must be zero over a complete cycle. Therefore, over a complete cycle .
      ::在一个实用的热力引擎中,内部能量的改变必须在整个周期内为零。 因此,在一个完整周期内为零。
    • The work done by a gas during a portion of a cycle = , note can be positive or negative.
      ::气体在某一周期的某一部分中完成的工作 =,注可以是正的,也可以是负的。

    Gas Heat Engines
    ::燃气热热引擎

    • When gas pressure-forces are used to move an object then work is done on the object by the expanding gas. Work can be done on the gas in order to compress it.
      ::当气体压力力用于移动物体时,扩展的气体会对该物体进行工作。可以对气体进行压缩。
    • If you plot pressure on the vertical axis and volume on the horizontal axis (see diagrams in the last chapter), the work done in any complete cycle is the area enclosed by the graph. For a partial process, work is the area underneath the curve, or.
      ::如果您在水平轴上绘制垂直轴和体积的压力图(见上一章的图表),则在任何完整循环中完成的工作是图中附加的区域。对于部分过程,工作是曲线下的区域,或。

    Question : A heat engine operates at a temperature of . The work output is used to drive a pile driver, which is a machine that picks things up and drops them. Heat is then exhausted into the atmosphere, which has a temperature of .
    ::问题:热引擎在温度下运行。 工作输出被用于驱动一个堆积驱动器, 即一台接收和丢弃物的机器。 然后热力被排入大气中, 大气中温度为...。

    a) What is the ideal efficiency of this engine?
    :sada) 该发动机的理想效率是什么?

    b.) The engine drives a weight by lifting it in . What is the engine’s power output?
    :sadb) 发动机通过举起来驱动重量。发动机的功率输出是多少?

    c) If the engine is operating at of ideal efficiency, how much power is being consumed?
    :sadc) 如果发动机以理想效率运行,耗电多少?

    d) The fuel the engine uses is rated at . How many kg of fuel are used in one hour?
    :sadd) 发动机使用的燃料定级为.一小时使用多少公斤燃料?

    Answer :
    ::答复:

    a) We will plug the known values into the formula to get the ideal efficiency.
    :sada) 我们将将已知值插入公式,以取得理想效率。

    b) To find the power of the engine, we will use the power equation and plug in the known values.
    :sadb) 为了找到发动机的动力,我们将使用电方程并插入已知值。

    c) First, we know that it is operating at of ideal efficiency. We also know that the max efficiency of this engine is . So the engine is actually operating at
    :sadc) 首先,我们知道它正在以理想效率运作,我们也知道,这个发动机的最大效率是......。

    of efficiency. So is of what?
    ::效率 效率 效率 效率 效率 效率 效率 效率 效率 效率 效率 效率 效率 效率 效率 的 效率 的 效率 。 那什么 效率 的 效果 呢 呢 ?

    Thermodynamics and Heat Engines Problem Set

    1. Consider a molecule in a closed box. If the molecule collides with the side of the box, how is the force exerted by the molecule on the box related to the momentum of the molecule? Explain conceptually, in words rather than with equations.
      ::在封闭框中考虑一个分子。 如果分子与盒的侧面相撞, 则盒中的分子所施加的强度与分子的动量有何关系? 用概念来解释, 用文字来解释, 而不是用方程式来解释 。
    2. If the number of molecules is increased, how is the pressure on a particular area of the box affected? Explain conceptually, in words rather than with equations.
      ::如果分子数量增加,盒子某一区域的压力如何受到影响?用文字而不是方程式从概念上解释。
    3. The temperature of the box is related to the average speed of the molecules. Use momentum principles to relate temperature to pressure. Explain conceptually, in words rather than with equations.
      ::框的温度与分子的平均速度有关。 使用动量原则将温度与压力联系起来。 用概念来解释, 用文字来解释, 而不是用方程式来解释 。
    4. What would happen to the number of collisions if temperature and the number of molecules remained fixed, but the volume of the box increased? Explain conceptually, in words rather than with equations.
      ::如果温度和分子数量保持不变,但盒子的体积却在增加,那么碰撞次数会怎样?用文字而不是方程式从概念上解释。
    5. Use the reasoning in the previous four questions to qualitatively derive the ideal gas law.
      ::利用前四个问题中的推理,从质量上得出理想天然气法。
    6. Typical room temperature is about . As you know, the air in the room contains both and gases, with nitrogen the lower mass of the two. If the average kinetic energies of the oxygen and nitrogen gases are the same (since they are at the same temperature), which gas has a higher average speed?
      ::典型的房间温度是...。如你所知,室内空气中既有气体,也有气体,其中氮含量较低。如果氧气和氮气的平均动能相同(因为温度相同),哪种气体的平均速度更高?
    7. Use the formula to argue why it is easier to pop a balloon with a needle than with a finger (assume you don’t have long fingernails).
      ::使用公式来解释为什么用针头弹出气球比用手指弹出气球更容易(假设你的指甲没有长指甲)。
    8. Take an empty plastic water bottle and suck all the air out of it with your mouth. The bottle crumples. Why, exactly, does it do this?
      ::用一个空塑料水瓶,用你的嘴吸吸所有的空气。
    9. You will notice that if you buy a large drink in a plastic cup, there will often be a small hole in the top of the cup, in addition to the hole that your straw fits through. Why is this small hole necessary for drinking?
      ::你会注意到,如果你在塑料杯中购买大杯饮料,除了你的稻草穿透的洞外,杯子顶部通常还会有一个小洞。为什么这个小洞是饮用的?
    10. Suppose you were swimming in a lake of liquid water on a planet with a lower gravitational constant than Earth. Would the pressure meters under the surface be the same, higher, or lower, than for the equivalent depth under water on Earth? (You may assume that the density of the water is the same as for Earth.)
      ::假设你在一个引力常数比地球低的行星上游在一个液态水湖中。 地表下的压力计是否与地球上水下同等深度相同、更高或更低? (你可以假定水的密度与地球相同)。
    11. Why is it a good idea for Noreen to open her bag of chips before she drives to the top of a high mountain?
      ::为什么诺琳在开到高山顶前 打开她的薯片袋是个好主意?
    12. Explain, using basic physics conservation laws, why the following conditions would cause the ideal gas law to be violated:
      1. There are strong intermolecular forces in the gas.
        ::气体中含有很强的分子分子力量。
      2. The collisions between molecules in the gas are inelastic.
        ::气体中分子之间的碰撞是无弹性的。
      3. The molecules are not spherical and can spin about their axes.
        ::这些分子不是球形分子,可以绕轴旋转。
      4. The molecules have non-zero volume.
        ::这些分子的体积不为零。

      To the right is a graph of the pressure and volume of a gas in a container that has an adjustable volume. The lid of the container can be raised or lowered, and various manipulations of the container change the properties of the gas within. The points and represent different stages of the gas as the container undergoes changes (for instance, the lid is raised or lowered, heat is added or taken away, etc.) The arrows represent the flow of time. Use the graph to answer the following questions.
      ::右边是气体在容器内的压力和体积图,容器的容积可调整。容器的盖子可以提高或降低,容器的各种操纵可以改变容器内气体的特性。当容器发生改变时,这些点和气体的不同阶段代表气体的不同阶段(例如,盖子提高或降低,加热或取走等等)。箭头代表时间的流。使用图表回答下列问题。


      ::使用基本的物理保护法解释为什么下列条件会导致违反理想的气体法: 气体中存在很强的中间分子力。 气体中分子之间的碰撞是无弹性的。 分子不是球状的, 可以在轴上旋转。 分子的体积不为零。 右边是具有可调整体积的容器中气体的压力和体积的图表。 容器的盖子可以升高或降低, 容器的各种操纵可以改变气体的特性。 当容器发生变化时, 这些点和气分代表气体的不同阶段( 例如, 盖子被抬高或降低, 热被添加或带走等 ) 箭头代表时间的流。 使用图表回答下列问题 。
    13. Consider the change the gas undergoes as it transitions from point to point . What type of process is this?
      1. adiabatic
        ::a/ diablibat 数据交换器
      2. isothermal
        ::异热热
      3. isobaric
        ::异乙酸
      4. isochoric
        ::异异地
      5. entropic
        ::赤道几内亚

      ::考虑气体在从点向点过渡时发生的变化。这是哪种过程?
    14. Consider the change the gas undergoes as it transitions from point to point . What type of process is this?
      1. adiabatic
        ::a/ diablibat 数据交换器
      2. isothermal
        ::异热热
      3. isobaric
        ::异乙酸
      4. isochoric
        ::异异地
      5. none of the above
        ::以上无一情况

      ::考虑气体在从点向点过渡时发生的变化。这是哪种过程?
    15. Consider the change the gas undergoes as it transitions from point to point . Which of the following best describes the type of process shown?
      1. isothermal
        ::异热热
      2. isobaric
        ::异乙酸
      3. isochoric
        ::异异地

      ::考虑气体在从点向点过渡时发生的变化。以下哪一种最能描述所显示的工艺类型?
    16. How would an isothermal process be graphed on a diagram?
      ::如何在图表上绘制地热过程图?
    17. Write a scenario for what you would do to the container to make the gas within undergo the cycle described above.
      ::写一个设想方案,说明您会对容器做些什么,以便在上述周期内制造气体。
    18. Antonio is heating water on the stove to boil eggs for a picnic. How much heat is required to raise the temperature of his 10.0 kg vat of water from to ?
      ::Antonio在炉子上加热水煮鸡蛋野餐,
    19. Amy wishes to measure the specific heat capacity of a piece of metal. She places the 75-g piece of metal in a pan of boiling water, then drops it into a styrofoam cup holding 50 g of water at . The metal and water come to an equilibrium temperature of . Calculate:
      1. The heat gained by the water
        ::海水的热量
      2. The heat lost by the metal
        ::金属丢失的热量
      3. The specific heat of the metal
        ::金属的具体热量

      ::Amy想测量一块金属的具体热容量。 她将75克金属块放在一个沸水锅里, 然后将它扔入一个泡沫杯里, 里面有50克的水。 金属和水的平衡温度是...。 计算: 水产生的热量。 金属失去的热量。 金属的具体热量。
    20. John wishes to heat a cup of water to make some ramen for lunch. His insulated cup holds 200 g of water at . He has an immersion heater rated at 1000 W (1000 J/s) to heat the water.
      1. How many JOULES of heat are required to heat the water to ?
        ::需要多少热量才能把水热到?
      2. How long will it take to do this with a 1000-W heater?
        ::用1000瓦加热器要多久?
      3. Convert your answer in part b to minutes.
        ::将回答的 b 部分转换为分钟 。

      ::约翰想加热一杯水 做一些拉面午餐。他的绝缘杯在 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
    21. You put a 20g cylinder of aluminum in the freezer . You then drop the aluminum cylinder into a cup of water at . After some time they come to a common temperature of . How much water was in the cup?
      ::然后把铝气瓶扔进水杯里。过了一段时间,它们就会达到共同的温度。杯子里有多少水?
    22. Emily is testing her baby’s bath water and finds that it is too cold, so she adds some hot water from a kettle on the stove. If Emily adds 2.00 kg of water at to 20.0 kg of bath water at , what is the final temperature of the bath water?
      ::Emily正在测试婴儿的洗澡水,发现水太冷,所以她从炉子上的水壶里加了热水。 如果Emily在20.0公斤的洗澡水中加了2公斤的水,那么浴水的最后温度是多少?
    23. You are trying to find the specific heat of a metal. You heated a metal in an oven to . Then you dropped the hot metal immediately into a cup of cold water. To the right is a graph of the temperature of the water versus time that you took in the lab. The mass of the metal is 10g and the mass of the water is 100g. Recall that water has a specific heat of .
      ::您正在寻找金属的具体热量。 您将金属加热在烤箱中, 然后将热金属立即丢入冷水杯中。 右边是水温度和实验室时间的图表。 金属质量为10克, 水质量为100克。 请记住水有特定的热量 。
    24. How much heat is required to melt a 20 g cube of ice if
      1. the ice cube is initially at
        ::最初的冰块
      2. the ice cube is initially at (be sure to use the specific heat of ice)
        ::最初的冰块( 一定要使用特定的冰热) 。

      ::融化20克冰块需要多少热量才能熔化,如果冰块最初是在冰块上(一定要使用特定的冰热)
    25. A certain alcohol has a specific heat of and a melting point of . You have a 150 g cup of liquid alcohol at and then you drop a 10 g frozen piece of alcohol at into it. After some time the alcohol cube has melted and the cup has come to a common temperature of .
      1. What is the latent heat of fusion (i.e. the ‘’ in the equation) for this alcohol?
        ::这种酒精的潜在聚变热(即方程中的核聚变热)是什么?
      2. Make a sketch of the graph of the alcohol’s temperature vs. time
        ::绘制酒精温度与时间的图表草图
      3. Make a sketch of the graph of the water’s temperature vs. time
        ::绘制水温度与时间的图表草图

      ::某种酒精有特定的热度和熔点 。 您有一个150克的液态酒精杯, 然后把10克的冰冻酒精杯放进去。 一段时间后, 酒精立方体融化了, 杯子也到了普通的温度 。 这种酒精的潜在聚变热( 也就是方程中的 ) 是什么 ? 绘制酒精温度与时间的图表的草图。 时间 绘制水温与时间的图表的草图 。
    26. Calculate the average speed of molecules at room temperature . (Remember from your chemistry class how to calculate the mass (in ) of an molecule.)
      ::计算室温度下分子的平均速度 。 (从您的化学类中记住如何计算分子的质量( 以 ) 。 )
    27. How high would the temperature of a sample of gas molecules have to be so that the average speed of the molecules would be % the speed of light?
      ::气体分子样本的温度要高到多少才能使分子的平均速度为光速的%?
    28. If a man weighing 50 kg stands on one foot, how much pressure is he exerting on the floor? Assume his foot is a rectangle 5 cm wide and 30 cm long.)
      ::如果一个体重50公斤的男子站在一只脚上,那么他在地板上施压多少?假设他的脚长5厘米宽,长30厘米,长5厘米长的矩形。 ))
    29. Calculate the amount of force exerted on a patch of your skin due to atmospheric pressure . Why doesn’t your skin burst under this force?
      ::计算由于大气压力对皮肤部位施加的强度。 为什么皮肤没有在这种压力下破裂?
    30. Use the ideal gas law to estimate the number of gas molecules that fit in a classroom with a length of 10 meters, a width of 9 meters, and a height of 5 meters.
      ::使用理想的天然气法来估计符合教室的气体分子数量,教室长度为10米,宽度为9米,高度为5米。
    31. Assuming that the pressure of the atmosphere decreases exponentially as you rise in elevation according to the formula , where is the atmospheric pressure at sea level , is the altitude in km and a is the scale height of the atmosphere .
      1. Use this formula to determine the change in pressure as you go from San Francisco to Lake Tahoe, which is at an elevation approximately above sea level.
        ::使用这个公式来确定从旧金山到Tahoe湖的压力变化,Tahoe湖的海拔大约高于海平面。
      2. If you rise to half the scale height of Earth’s atmosphere, by how much does the pressure decrease?
        ::如果升到地球大气高度的一半,压力会降低多少?
      3. If the pressure is half as much as on sea level, what is your elevation?
        ::如果压力是海平面压力的一半 你的海拔是多少?

      ::假设大气压力随着你根据公式(海平面的大气压力在何处)升起而指数性地下降,则大气的高度是千米,而大气的高度是比例高度。使用这个公式来确定从旧金山到塔霍湖的压力变化。塔霍湖大约在海平面之上。如果你升到地球大气的高度的一半,压力会降多少?如果压力是海平面的一半,那么你的高度是什么?
    32. The following experiment was conducted by a professor at a university. A rock was dropped from the roof of the lab and, with expensive equipment, was observed to gain of internal energy. The professor explained to his students that the law of conservation of energy required that if he put of heat into the rock, the rock would then rise to the top of the building. When this did not occur, the professor declared the law of conservation of energy invalid. Was the law of conservation of energy violated in this experiment, as was suggested? Explain. If the law wasn’t violated, then why didn’t the rock rise?
      ::下面的实验是由大学的一位教授进行的。从实验室屋顶上扔下一块岩石,用昂贵的设备观察到获得内部能源。教授向其学生解释说,节能法要求,如果他把热量放入岩石,岩石就会升至建筑物顶部。 如果这没有发生,教授宣布节能法无效。 教授宣布,节能法在试验中是否如建议的那样违反了节能法? 解释。如果法律没有被违反,那么为什么没有上升?
    33. An instructor has an ideal monatomic helium gas sample in a closed container with a volume of , a temperature of , and a pressure of .
      1. Approximately how many gas atoms are there in the container?
        ::集装箱内大约有几颗气体原子?
      2. Calculate the mass of the individual gas atoms.
        ::计算单个气体原子的质量。
      3. Calculate the speed of a typical gas atom in the container.
        ::计算容器中典型气体原子的速度。
      4. The container is heated to . What is the new gas pressure?
        ::容器加热了,新的气体压力是什么?
      5. While keeping the sample at constant temperature, enough gas is allowed to escape to decrease the pressure by half. How many gas atoms are there now?
        ::在将样品保持在恒定温度的同时,有足够的气体可以逃脱,将压力减半。 现在有多少气原子?
      6. Is this number half the number from part (a)? Why or why not?
        ::这是(a)部分数字的一半吗?为什么或为什么不是?
      7. The closed container is now compressed isothermally so that the pressure rises to its original pressure. What is the new volume of the container?
        ::封闭的容器现在压缩了,是热压,使压力上升到原来的压力。 容器的新体积是多少?
      8. Sketch this process on a P-V diagram.
        ::在P-V图中绘制这个过程。
      9. Sketch cubes with volumes corresponding to the old and new volumes.
        ::与旧卷和新卷相对应的卷缩立方体。

      ::教官在封闭容器中拥有一个理想的月度气样本,该容器的体积为 、 温度和压力 。 估计容器内有多少气体原子? 计算单个气体原子的质量 。 计算容器内一个典型气体原子的速度 。 容器的热度是多少? 新的气体压力是多少? 在保持恒定温度时, 有足够的气体可以逃脱一半的压力 。 现在有多少气原子? 有多少气原子? 这是来自(a) 部分的数字的一半吗? 为什么不是? 封闭容器现在压缩起来是为了让压力上升到原来的压力。 容器的新体积是什么? 在P- V 图上将这个过程拖到什么? 与旧的和新体积相应的体积的蒸馏器。
    34. A famous and picturesque dam, high, releases of water a second. The water turns a turbine that generates electricity.
      1. What is the dam’s maximum power output? Assume that all the gravitational potential energy of the water is converted into electrical energy.
        ::水坝的最大发电量是什么? 假设水的所有引力潜力都转化为电力能源。
      2. If the turbine only operates at % efficiency, what is the power output?
        ::如果涡轮机的功率只有%,那么电输出是多少?
      3. How many Joules of heat are exhausted into the atmosphere due to the plant’s inefficiency?
        ::有多少热量因工厂效率低下而排入大气层?


      ::一个有名的、光滑的大坝,水的高度释放。水是发电的涡轮机。大坝的最大功率是多少?假设水的所有引力潜力都转化为电力能源。 如果涡轮只有百分之一的功率,那么发电量是多少?有多少热能因电厂效率低下而耗尽了大气?
    35. A heat engine operates at a temperature of . The work output is used to drive a pile driver, which is a machine that picks things up and drops them. Heat is then exhausted into the atmosphere, which has a temperature of .
      1. What is the ideal efficiency of this engine?
        ::这个引擎最理想的效率是什么?
      2. The engine drives a weight by lifting it in . What is the engine’s power output?
        ::引擎通过举起来驱动重量。 引擎的动力输出是什么?
      3. If the engine is operating at % of ideal efficiency, how much power is being consumed?
        ::如果发动机运转效率达到理想效率的%,那么消耗多少电力?
      4. How much power is exhausted?
        ::耗竭了多少电力?
      5. The fuel the engine uses is rated at . How many kg of fuel are used in one hour?
        ::发动机使用的燃料定级为.一小时使用多少公斤燃料?

      ::热引擎在温度下运行 。 工作输出用于驱动一个堆积驱动器, 即一个把东西捡起来丢掉的机器。 然后热被排入大气, 温度为 。 最理想的这个引擎效率是多少? 发动机通过提升引擎来驱动重量。 发动机的动力输出是什么? 如果发动机以理想效率的%运转, 电能消耗多少? 耗竭多少? 发动机使用的燃料是定级的 。 一小时内使用多少公斤的燃料?
    36. Calculate the ideal efficiencies of the following sci-fi heat engines:
      1. A nuclear power plant on the moon. The ambient temperature on the moon is . Heat input from radioactive decay heats the working steam to a temperature of .
        ::月球上的核电厂 月球上的环境温度是 放射性衰变的热量 将工作蒸汽热到温度
      2. A heat exchanger in a secret underground lake. The exchanger operates between the bottom of a lake, where the temperature is , and the top, where the temperature is .
        ::地下秘密湖中的热交换器。交换器在湖底,温度在湖底,温度在湖顶,温度在湖顶之间。
      3. A refrigerator in your dorm room at Mars University. The interior temperature is ; the back of the fridge heats up to .
        ::在火星大学宿舍的冰箱里 室内温度是...

      ::计算以下 sci-fi 热引擎的理想效率: 月球上的核电厂。 月球上的环境温度是 . 放射性衰变的热输入将工作蒸汽热到 . 秘密地下湖中的热交换器。 交换器在湖底, 温度在湖底, 温度在湖顶, 温度在湖顶。 火星大学的宿舍里有冰箱。 室内温度在 ; 冰箱的后面热到 。
    37. How much external work can be done by a gas when it expands from to in volume under a constant pressure of ? Can you give a practical example of such work?
      ::当气体在不断的压力下从数量扩大到数量时,它能做多少外部工作? 你能举出这种工作的实际例子吗?
    38. In the above problem, recalculate the work done if the pressure linearly decreases from to under the same expansion. Hint: use a diagram and find the area under the line.
      ::在上述问题中,如果压力线性从同一扩展线向下下降,则重新计算完成的工作。提示:使用图表并找到线下的区域。
    39. One mole of an ideal gas is moved through the following states as part of a heat engine. The engine moves from state A to state B to state C, and then back again. Use the Table ( ) to answer the following questions:
      1. Draw a P-V diagram.
        ::绘制 P- V 图表 。
      2. Determine the temperatures in states A, B, and C and then fill out the table.
        ::确定A、B和C国的温度,然后填写表格。
      3. Determine the type of process the system undergoes when transitioning from A to B and from B to C. (That is, decide for each if it is isobaric, isochoric, isothermal, or adiabatic.)
        ::确定系统从A向B和从B向C过渡时所经历的流程类型。 (即决定每个系统是异巴里、异地、异地热、异地热还是异地。 )
      4. During which transitions, if any, is the gas doing work on the outside world? During which transitions, if any, is work being done on the gas?
        ::天然气在外部世界工作,在哪些过渡期间(如果有的话)?在哪些过渡期间(如果有的话),在哪些过渡期间(如果有的话),在哪些过渡期间(如果有的话),在哪些过渡期间(如果有的话)在天然气方面开展工作?
      5. What is the amount of net work being done by this gas?
        ::这种气体净工作量是多少?

      ::理想气体的一个摩尔作为热力引擎的一部分通过下列状态移动。 引擎从 A 状态向 B 状态向 C 状态移动, 然后再返回。 使用表 () 回答下列问题 : 绘制 P- V 图表 。 确定 A 、 B 和 C 状态的温度, 然后填上表格 。 确定系统从 A 向 B 和 B 向 C 过渡时所经历的工艺类型 。 ( 也就是说, 决定每种工艺是否为异端、 偏执、 异热或对称 。 ) 气体在外部世界工作, 在哪些过渡期间( 如果有的话) 该气体的工作正在进行? 该气体的净工作量是多少 ?
    State Volume Pressure Temperature
    A
    B
    C
    1. A sample of gas is used to drive a piston and do work. Here’s how it works:
      • The gas starts out at standard atmospheric pressure and temperature. The lid of the gas container is locked by a pin.
        ::气体从标准大气压力和温度开始,气体容器的盖子被钉子锁住。
      • The gas pressure is increased isochorically through a spigot to twice that of atmospheric pressure.
        ::气体压力通过一个源头在异地上增加至大气压力的两倍。
      • The locking pin is removed and the gas is allowed to expand isobarically to twice its volume, lifting up a weight. The spigot continues to add gas to the cylinder during this process to keep the pressure constant.
        ::锁针被拆除,气体被允许以同位素方式膨胀到其体积的两倍,从而提升了重量。 在这一过程中,Spigot继续在气瓶中添加气体,以保持压力不变。
      • Once the expansion has finished, the spigot is released, the high-pressure gas is allowed to escape, and the sample settles back to .
        ::高压气体被允许逃逸 样品又回到了原位
      • Finally, the lid of the container is pushed back down. As the volume decreases, gas is allowed to escape through the spigot, maintaining a pressure of . At the end, the pin is locked again and the process restarts.
        ::最后,容器盖被往后拉。随着体积的下降,气体可以通过螺旋体逃逸,保持压力。最后,针被再次锁住,程序重新开始。
      1. Draw the above steps on a diagram.
        ::在图表中绘制上述步骤。
      2. Calculate the highest and lowest temperatures of the gas.
        ::计算气体的最高和最低温度。

      ::一种气体样本被用于驱动活塞和工作。 这就是它是如何工作的。 气体在标准大气压力和温度下启动。 气体容器盖盖由针锁定。 气体压力通过螺旋增加, 是大气压力的两倍。 锁针被移走, 气体允许以烟雾方式膨胀到其体积的两倍, 提升一个重量。 螺旋在这个过程中继续将气体添加到气瓶中以保持压力不变。 一旦扩展完成, 螺旋就会释放, 高气压气体就会被放出, 样品会稳定下来 。 最后, 容器盖会被推回。 随着气压的减少, 气体可以从螺旋体中逃出, 保持一个压力 。 在最后, 针被再次锁定, 过程会重新开始 。 在图表上绘制上面的步伐 。 计算气体的最高和最低温度 。
    2. A heat engine operates through cycles according to the diagram sketched below. Starting at the top left vertex they are labeled clockwise as follows: a, b, c, and d.
      1. From the work is and the change in internal energy is ; find the net heat.
        ::从工作开始,内部能量的变化是, 找到净热。
      2. From the a-c the change in internal energy is . Find the net heat from b-c.
        ::从 a - c 中发现内部能量的变化是。 从 b - c 中找到净热 。
      3. From c-d the work is . Find the net heat from c-d-a.
        ::找到C -d -a的净热量
      4. Find the net work over the complete cycles.
        ::在整个周期中找到净工作。
      5. The change in internal energy from b-c-d is . Find:
        1. the net heat from c-d
          ::C-d的净热量
        2. the change in internal energy from d-a
          ::从 d-a 变化的内部能量
        3. the net heat from d-a
          ::d-a的净热量

        ::从 b- c- d 内部能量的变化。 查找: 从 c- d 内部能量的变化, 从 d- a 内部能量的变化, 从 d- a 的净热变化 。


      ::热引擎根据下面绘制的图表通过循环运行。从左上端的顶部顶端开始,它们按以下时钟标记如下:a、b、c和d。从工作开始,内部能量的变化是;找到净热;从a-c到内部能量的变化是。从 b-c到内部能量的变化是。从 c-d到工作,从 c-d到工作。从 c-d-a到整个周期的净热。从c-d到净工作。从b-c-d到内部能量的变化是:从c-d到内部能量的变化是净热,从d-a到d-a,从d-a到内部能量的变化是净热。从b-c-d到内部能量的变化是净热,从c-d-a到d-a。
    3. A sample mole of an ideal gas is taken from state A by an isochoric process to state B then to state C by an isobaric process. It goes from state C to D by a process that is linear on a diagram, and then it goes back to state A by an isobaric process. The volumes and pressures of the states are given in the Table ( ); use this data to complete the following:
      1. Find the temperature of the states
        ::查找状态的温度
      2. Draw a diagram of the process
        ::绘制进程图
      3. Find the work done in each of the four processes
        ::查找在四个进程中每个进程中完成的工作
      4. Find the net work of the engine through a complete cycle
        ::通过整个周期查找引擎的净工作
      5. If of heat is exhausted in D-A and A-B and C-D are adiabatic, how much heat is inputted in B-C?
        ::如果D-A、A-B和C-D的热耗尽,那么B-C输入的热量是多少?
      6. What is the efficiency of the engine?
        ::引擎效率如何?

      ::从A国取出理想气体的样本摩尔,用异地法过程从A国取出,用异地法过程给B国取出,然后用异地法过程给C国取出。从C国到D国取出,用图表线性,然后用异地法过程回溯到A国。表格中列出了各州的量和压力(;);使用这些数据来完成以下内容: 查找各州的温度 绘制一个过程的图表 绘制一个过程的图 找出四个过程中每个过程完成的工作 在整个循环中找到引擎的净工作 如果D-A国和A-B国及C-D国的热耗尽了,那么B-C输入的热量是多少? 引擎的效率是多少?
    state Volume in Pressure in
    A
    B
    C
    D