Question

Some hydrogen gas is enclosed within a chamber being held at 200∘C whose volume is 0.0250 m3. Initially, the pressure in the gas is 1.50×106Pa (14.8 atm). The chamber is removed from the heat source and allowed to cool until the pressure in the gas falls to 0.950×106Pa. At what temperature T2 does this occur?

Answer 1

The final temperature of the gas is $27^{\circ}C$

Explanation:

Since the volume of the gas is constant (the volume of the chamber does not  change), we can apply the pressure's law, which states that:

"For a gas kept at constant volume, the pressure of the gas is proportional to its absolute temperature"

Mathematically:

$\frac{p}{T}=const.$

where

p is the gas pressure

T is its Kelvin temperature

For this problem, the equation can be written as

$\frac{p_1}{T_1}=\frac{p_2}{T_2}$

where we have:

$p_1=1.50\cdot 10^6 Pa$ is the initial pressure

$p_2=0.950\cdot 10^6 Pa$ is the final pressure

$T_1=200^{\circ}C+273=473 K$ is the initial temperature

$T_2$ is the final temperature

And solving for T2,

$T_2=\frac{p_2 T_1}{p_1}=\frac{(0.950\cdot 10^6)(473)}{1.50\cdot 10^6}=300 K$

So the final temperature is

$T_2 = 300 K - 273 = 27^{\circ}C$

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