Question

Think Critically Predict what would happen to the volume of a gas
if the pressure on that gas were doubled and then the absolute
temperature of the gas were doubled.

Answer 1

The volume of the gas does not change

Explanation:

To solve this problem, we can apply the ideal gas equation, which states that:

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

where

p is the pressure of the gas

V is its volume

T is its absolute temperature

The equation can also be written as

$\frac{p_1 V_1}{T_1}=\frac{p_2 V_2}{T_2}$

where in this problem we have:

$p_1$ is the initial pressure of the gas

$V_1$ is the initial volume

$T_1$ is the initial temperature

$p_2 = 2 p_1$ is the final pressure (twice the initial pressure)

$V_2$ is the final volume

$T_2 = 2T_1$ is the final temperature (twice the initial temperature)

Solving for V2, we find what happens to the volume of the gas:

$V_2 = \frac{p_1 V_1 T_2}{p_2 T_1}=\frac{p_1 V_1 (2T_1)}{(2p_1) T_1}=V_1$

Therefore, the volume of the gas does not change.

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