10.4 联合天然气法

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  联合天然气法

  

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  In order to design hot air balloons like these, engineers must make gas law calculations, calculations, and have knowledge of the density of air at different altitudes.
  ::为了设计这种热气球,工程师必须进行气体定律计算、计算,并了解不同高度的空气密度。

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  Combined Gas Law
  ::联合天然气法

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  For a given quantity of gas, it has been found experimentally that the volume of the gas is inversely proportional to the pressure applied to the gas when the is kept constant. That is,
  ::对于一定数量的气体,实验发现气体的体积与气体保持恒定时的压力成反比。也就是说,

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  $$\begin{array}{r}V\propto \frac{1}{P}\text{at a constant}T.\end{array}$$

  
  ::V1P 常数 T 。

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  For example, if the pressure on a gas is doubled, the volume is reduced to half its original volume. This relationship is known as Boyle’s Law .  Boyle’s Law can also be written  $\begin{array}{r}PV=\text{constant}\end{array}$ at constant $\begin{array}{r}T\end{array}$ . As long as the temperature and the amount of gas remains constant, any variation in the pressure or volume will result in a change in the other one, keeping the product at a constant value.
  ::例如,如果气体的压力加倍,其体积将减少到原来的体积的一半。 这种关系被称为Boyle的法律。 Boyle的法律也可以写成PV=contable at stand T。 只要温度和气体数量保持不变,压力或体积的任何变化都会导致另一体的改变,使产品保持不变值。

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  Pressures are given in a multitude of units. We've already discussed Pascals, and we know that another unit for pressure is the atmosphere (1 atm = 101.3 x 10 ³ Pa). The third commonly used pressure unit is the torr (symbol: Torr). 760 torr is 1 atm, but 1 torr is also the increase in pressure necessary to cause liquid mercury to rise by 1 mm. For that reason, torr is also commonly referred to as "millimeters mercury." Another pressure unit commonly used in our everyday world is psi, or pounds per square inch, though neither psi nor torr are SI units.
  ::压力是由多个单位给出的。 我们已经讨论过帕斯卡尔, 我们知道另一个压力单位是大气(1 atm = 101.3 x 103 pa) 。 第三个常用的压力单位是托尔( 符号: Torr) 。 760 orrr 是 1 atm 。 但是 1 orrr 也是 增加 所需的压力, 使液体汞增加 1 毫米。 因此, 托拉尔通常也被称为 “ 毫米汞 ” 。 我们日常使用的另一个压力单位是 psi , 或 磅/ 平方英寸, 尽管 psi 和 torrr 都不是 SI 单位 。

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  Temperature also affects the volume of a gas. Jacques Charles found that when the pressure is held constant, the volume of a gas increases in direct proportion to its absolute temperature. This relationship became known as Charles’ Law .
  ::温度也会影响气体的体积。 雅克·查尔斯发现,当压力保持不变时,气体的体积会与绝对温度成正比地增加。 这种关系被称为查尔斯法(Charles Law ) 。

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  $$\begin{array}{r}V\propto T\text{at constant}P.\end{array}$$

  
  ::静态P. V. T.

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  A third gas law, known as Gay-Lussac’s Law , states that at constant volume, the pressure of a gas is directly proportional to the absolute temperature.
  ::第三种气体法,即《同性恋-卢萨克法》规定,气体的压力在恒定体积下与绝对温度直接成正比。

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  $$\begin{array}{r}P\propto T\text{at constant}V.\end{array}$$

  
  ::PT 常数V。

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  The kinetic-molecular theory assumes that there are no attractive forces between the molecules and that the volume of the molecules themselves is negligible compared to the volume of the gas. At high temperatures and low pressures, these assumptions are true and the gases follow the gas laws very accurately. However, these three laws are true only as long as the pressure and density are relatively low. When a gas is compressed to the point that the molecular volume is a significant portion of the gas volume, the gas laws begin to fail.  Similarly, when gases become so dense that the molecules begin to attract each other, the gas laws also fail. These changes are expressed in the Van der Waals equations. 
  ::动能分子理论假定分子之间没有吸引力,分子本身的体积与气体的体积相比是微不足道的。在高温和低压下,这些假设是真实的,气体遵循气体法则非常准确。然而,这三项法律只有在压力和密度相对较低的情况下才属真实。当气体压缩到分子量占气体体积相当大的一部分时,气体法则就开始失效。同样,当气体变得如此稠密以致分子开始相互吸引时,气体法则也会失效。这些变化表现在Van der Waals的方程式中。

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  These three gas laws can be combined into the Combined Gas Law as follows:
  ::这三个天然气法可合并为《天然气联合法》,具体如下:

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  $$\begin{array}{r}PV\propto Tor\frac{PV}{T}=\text{constant}\end{array}$$

  
  ::PVT 或PVT = 常数

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  A commonly used form of the combined gas law states that, for a sample of gas, the ratio of the product of the original pressure and volume to the original temperature will equal the ratio of the product of a new pressure and volume to the new temperature, or
  ::一种常用的综合天然气法形式规定,对于天然气样本,原压力和体积与原温度之比等于新压力和体积与新温度之比,或

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  $$\begin{array}{r}\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}.\end{array}$$

  
  ::P1V1T1=P2V2。

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  This equation is useful when operating with the same sample of gas, and given five of the variables, to solve for the sixth.
  ::这个方程式在使用相同的气体样本操作时非常有用, 并给出了五个变量, 用于解决第六个变量 。

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  When solving problems with temperature in them, the calculations require that temperatures be in Kelvin. Be careful to convert to Kelvin when given temperatures in Celsius.
  ::当解决温度问题时,计算要求温度在开尔文。 当给定温度为摄氏度时要小心转换为开尔文 。

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  Example  
  ::示例示例示例示例

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  A sample of gas has a volume of 2.00 L and a pressure of 0.750 kPa when its temperature is 25°C. If the volume is expanded to 4.00 L and the pressure reduced to 0.500 kPa, what must the temperature become?
  ::气体样本的体积为2.00升,温度为25°C时压力为0.750千帕。 如果气体体积扩大到4.00升,压力减少到0.500千帕,温度会变成什么?

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  The relationships between volume and temperature and pressure and temperature expressed in the gas laws are only true when the of the molecules are directly proportional to the temperature.  Therefore, when dealing with all gas laws, the temperatures must be expressed in Kelvin.
  ::气体定律中表达的体积与温度、压力和温度之间的关系只有在分子与温度直接成正比时才是真实的。 因此,在处理所有气体定律时,温度必须以克尔文表示。

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  Given:
  ::参照:

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  $$\begin{array}{rl}{P}_1& =0.750kPa{P}_2=0.500kPa\\ V_1& =2.00L{V}_2=4.00L\\ T_1& =298K{T}_2=?\end{array}$$

  
  ::P1=0.750 kPAPP2=0.500 kPAV1=2.00 LV2=4.00 LT1=298 KT2=?

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  $$\begin{array}{r}{T}_2=\frac{P_2{V}_2{T}_1}{P_1{V}_1}=\frac{(0.500kPa)(4.00L)(298K)}{(0.750kPa)(2.00L)}=397K\end{array}$$

  
  ::T2=P2V2T1P1V1=(0.500千帕)(4.00 L)(298 K)(0.750千帕)(2.00 L)=397 K

  

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  Colorful helium-filled balloons add such a happy feeling to any special occasion but have you ever lost one of these balloons? It is so sad to watch it as it floats up to the sky. Did you ever wonder about how high it will go? Where will it travel to? Will it pop or sink to the ground at some point? Play around with the simulation below to learn more about the combined gas laws and find out what happens to a runaway balloon:
  ::任何特殊场合都有如此多色的充气球的喜悦感,但你是否曾经失去过其中的一个气球?当气球漂浮到天空时,看着它漂浮到天空时,你感到非常悲哀。你有没有想过气球会飞到多高?它会飞到哪里?它会弹出还是沉到地上?在某个时候它会弹出还是沉到地上?在下面的模拟中玩耍,以便更多地了解气体的混合定律,并找出一个失控气球会发生什么:

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  Further Reading
  ::继续阅读

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  • Gas Pressure and Force
    ::气压和气压

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  Summary
  ::摘要

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  • For a given quantity of gas, it has been found experimentally that the volume of the gas is inversely proportional to the pressure applied to the gas when the temperature is kept constant.
    ::对于一定数量的气体,实验发现气体的体积与温度保持恒定时气体的压力成反比。
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  • Boyle’s Law is $\begin{array}{r}V\propto \frac{1}{P}\text{at constant}T\end{array}$ .
    ::Boyle的法律是V1P 常数T。
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  • Charles’ Law is $\begin{array}{r}V\propto T\text{at constant}P\end{array}$ .
    ::查尔斯·法(Charles Law)在P常数P.
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  • Gay-Lussac’s law states that at constant volume, the pressure of a gas is directly proportional to the absolute temperature, $\begin{array}{r}P\propto T\text{at constant}V\end{array}$ .
    ::Gay-Lussac的法律规定,在恒定体积下,气体的压力与绝对温度直接成正比,PT在恒定V。
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  • These three gas laws can be combined into a so-called combined gas law,  $\begin{array}{r}\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}\end{array}$ .
    ::这三项天然气法可以合并为所谓的联合天然气法,即P1V1T1=P2V2T2。

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  Review
  ::回顾

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  1. A sample of gas has a volume of 800. mL at -23.0°C and 300. Torr.  What would the volume of the gas be at 227.0°C and 600. Torr?
     ::气体样本在-23.0°C和300°C时的容量为800毫升。 Torr. 气体在227.0°C和600°C的容量是多少? Torr?
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  2. 500.0 L of gas are prepared at 0.921 atm pressure and 200.0°C.  The gas is placed into a tank under high pressure.  When the tank cools to 20.0°C, the pressure is 30.0 atm.  What is the volume of the gas under these conditions?
     ::500.0升气体在0.921原子压力和200.0°C时制备。气体在高压下放入一个罐体。当罐体冷到20.0°C时,压力为30.0 °C。在这种条件下,气体的体积是多少?
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  3. What is the volume of gas at 2.00 atm and 200.0 K if its original volume was 300. L at 0.250 atm and 400.0 K?
     ::如果原气量为300,2,00 小时和2,00 公里的气体量是多少? 0.250 小时和 4,0 K 小时的气体量是300, L 小时和 4,0 K 小时?

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  Explore More
  ::探索更多

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  Use this resource to answer the questions that follow.
  ::使用此资源回答下面的问题 。

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  1. What must be held constant for the combined gas law to be true?
     ::联合天然气法要做到真实,必须保持什么不变?
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  2. What happens to the combined gas law if temperature, pressure, or volume are held constant?  
     ::如果温度、压力或体积保持恒定,