Course: 14.6 联合天然气法

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联合天然气法
What keeps things cold?
::是什么让事情变冷?

The modern refrigerator takes advantage of the laws to remove from a system . Compressed gas in the coils (see above) is allowed to expand. This expansion lowers the temperature of the gas and transfers heat energy from the material in the refrigerator to the gas. As the gas is pumped through the coils, the pressure on the gas compresses it and raises the gas temperature. This heat is then dissipated through the coils into the outside air. As the compressed gas is pumped through the system again, the process repeats itself.
::现代冰箱利用法律从一个系统中去除。允许圈内压缩气体( 见上文) 膨胀。气体的膨胀会降低气体的温度, 并将热能从冰箱中的材料转移到气体中。随着气体通过圈内抽气, 气体压压会增加气体的温度。然后, 气体通过圈内吸收气体进入外部空气。当压缩气体再次通过系统抽气时, 过程会重复。

Combined Gas Law
::联合天然气法

To this point, we have examined the relationships between any two of the variables of $\begin{align*}P\end{align*}$ , $\begin{align*}V\end{align*}$ , and $\begin{align*}T\end{align*}$ , while the third variable is held constant. However, situations arise where all three variables change. The combined gas law expresses the relationship between the pressure, volume , and absolute temperature of a fixed amount of gas. For a combined gas law problem, only the amount of gas is held constant.
::至此,我们研究了P、V和T等两个变量之间的关系,而第三个变量保持不变。然而,所有三个变量都发生变化,会出现三种情况。合并天然气法显示了固定气体数量的压力、数量和绝对温度之间的关系。对于合并天然气法问题,只有气体数量保持不变。

$\begin{aligned} \frac{P \times V}{T} = k and \frac{P_{1} \times V_{1}}{T_{1}} = \frac{P_{2} \times V_{2}}{T_{2}} \end{aligned}$
$\begin{align*}\frac{P \times V}{T}=k \quad \text{and} \quad \frac{P_1 \times V_1}{T_1}=\frac{P_2 \times V_2}{T_2}\end{align*}$
::PxVT = kandP1xV1T1 = P2xV2T2

Sample Problem: Combined Gas Law
::问题:联合天然气法

2.00 L of a gas at 35°C and 0.833 atm is brought to standard temperature and pressure (STP). What will be the new gas volume?
::在35°C和0.833 atm的气体中,将2.00升的气体带入标准温度和压力(STP),新的气体体积是多少?

Step 1: List the known quantities and plan the problem.
::第1步:列出已知数量并规划问题。

Known
::已知已知

$\begin{align*}P_1=0.833 \text{ atm}\end{align*}$
::P1=0.833 小时

$\begin{align*}V_1=2.00 \text{ L}\end{align*}$
::V1=2.00升

$\begin{align*}T_1=35^\circ \text{C}=308 \text{ K}\end{align*}$
::T1=35°C=308K

$\begin{align*}P_2=1.00 \text{ atm}\end{align*}$
::P2=1.00 小时

$\begin{align*}T_2=0^\circ \text{C}=273 \text{ K}\end{align*}$
::T2=0C=273K

Unknown
::未知

$\begin{align*}V_2=? \text{ L}\end{align*}$
::V2=L吗?

Use the combined gas law to solve for the unknown volume $\begin{align*}(V_2)\end{align*}$ . STP is 273 K and 1 atm. The temperatures have been converted to Kelvin.
::使用合并天然气法解决未知体积( V2) 。 STP为 273 K 和 1 atm 。温度已转换为 Kelvin 。

Step 2: Solve.
::步骤2:解决。

First, rearrange the equation algebraically to solve for $\begin{align*}V_2\end{align*}$ .
::首先,重新排列方程式代数以解析 V2 。

$\begin{aligned} V_{2} = \frac{P_{1} \times V_{1} \times T_{2}}{P_{2} \times T_{1}} \end{aligned}$
$\begin{align*}V_2=\frac{P_1 \times V_1 \times T_2}{P_2 \times T_1}\end{align*}$
::V2 = P1xV1xT2P2xT1

Now substitute the known quantities into the equation and solve.
::现在将已知数量替换为方程式和解析。

$\begin{aligned} V_{2} = \frac{0.833 atm \times 2.00 L \times 273 K}{1.00 atm \times 308 K} = 1.48 L \end{aligned}$
$\begin{align*}V_2=\frac{0.833 \text{ atm} \times 2.00 \text{ L} \times 273 \text{ K}}{1.00 \text{ atm} \times 308 \text{ K}}=1.48 \text{ L}\end{align*}$
::V2=0.833 AM×2.00 Lx273 K1.00 AM×308 K=1.48 L

Step 3: Think about your result.
::步骤3:想想你的结果。

Both the increase in pressure and the decrease in temperature cause the volume of the gas sample to decrease. Since both changes are relatively small, the volume does not decrease dramatically.
::压力的上升和温度的下降都导致气体样本量的下降,由于这两个变化相对较小,其数量并没有急剧下降。

It may seem challenging to remember all the different gas laws introduced so far. Fortunately, Boyle’s, Charles’s, and Gay-Lussac’s laws can all be easily derived from the combined gas law. For example, consider a situation where a change occurs in the volume and pressure of a gas while the temperature is being held constant. In that case, it can be said that $\begin{align*}T_1 = T_2\end{align*}$ . Look at the combined gas law and cancel the $\begin{align*}T\end{align*}$ variable out from both sides of the equation. What is left over is Boyle’s law :
::记住迄今为止引入的所有不同的天然气法似乎都具有挑战性。幸运的是,博伊勒、查尔斯和盖伊-卢萨克的法律都可以很容易地从联合天然气法中衍生出来。比如,考虑在温度保持恒定的情况下气体的体积和压力发生变化的情况。在这种情况下,可以说T1=T2,看看联合天然气法,从等式的两侧取消T变量。剩下的是博伊勒的法律:

$\begin{align*}P_1 \times V_1 = P_2 \times V_2\end{align*}$ . Likewise, if the pressure is constant, then $\begin{align*}P_1 = P_2\end{align*}$ and canceling $\begin{align*}P\end{align*}$ out of the equation leaves Charles’s law . If the volume is constant, then $\begin{align*}V_1 = V_2\end{align*}$ and canceling $\begin{align*}V\end{align*}$ out of the equation leaves Gay-Lussac’s law .
::P1xV1=P2xV2. 同样,如果压力不变,那么P1=P2并取消P出于方程式之外,就脱离了Charles的法律。如果数量不变,那么V1=V2并取消V出于方程式之外,Gay-Lussac的法律就脱离了Gay-Lussac的法律。

Summary
::摘要

The combined gas law shows the relationships among temperature, volume, and pressure.
::综合天然气法显示了温度、体积和压力之间的关系。

$\begin{align*}\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \end{align*}$
::P1V1T1=P2V2T2

Review
::回顾

What is the only thing held constant in a combined gas law problem?
::在天然气法的综合问题中,什么是唯一保持不变的东西?

If you want to solve for the volume of a gas $\begin{align*}(V_2)\end{align*}$ and $\begin{align*}P_1\end{align*}$ is greater than $\begin{align*}P_2\end{align*}$ , would you expect $\begin{align*}V_2\end{align*}$ to be larger or smaller than $\begin{align*}V_1\end{align*}$ ?
::如果您想要解答一个气体(V2)和P1的体积大于P2, 你会指望V2大于或小于V1吗?

What would be the equation for finding $\begin{align*}P_2\end{align*}$ given all the other parameters?
::鉴于所有其他参数,找到P2的方程是什么?

Section outline

General

联合天然气法

What keeps things cold? ::是什么让事情变冷?

Combined Gas Law ::联合天然气法

Sample Problem: Combined Gas Law ::问题:联合天然气法

Summary ::摘要

Review ::回顾

What keeps things cold?
::是什么让事情变冷?

Combined Gas Law
::联合天然气法

Sample Problem: Combined Gas Law
::问题:联合天然气法

Summary
::摘要

Review
::回顾