Question

How will the volume of a fixed sample of gas change if the pressure is doubled and its Celsius temperature is halved? How will the volume of a fixed sample of gas change if the pressure is doubled and its Celsius temperature is halved? The change cannot be determined without more specific information.

A. It will decrease by a factor of 4.
B. It will decrease by a factor of 2.
C. It will double.
D. It will remain constant.

Answer 1

Answer: The volume will decrease by a factor of 4.

Explanation:

To calculate the volume when temperature and pressure has changed, we use the equation given by combined gas law.

The equation follows:

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

where,

$P_1,V_1\text{ and }T_1$ are the initial pressure, volume and temperature of the gas

$P_2,V_2\text{ and }T_2$ are the final pressure, volume and temperature of the gas

We are given:

$P_1=P_1\\V_1=V_1\\T_1=T_1\\P_2=2P_1\\V_2=?\\T_2=\frac{T_1}{2}$

Putting values in above equation, we get:

$\frac{P_1\times V_1}{T_1}=\frac{2P_1\times V_2}{\frac{T_1}{2}}\\\\V_2=\frac{P_1\times V_1}{T_1}\times \frac{T_1}{4P_1}\\\\V_2=\frac{V_1}{4}$

Hence, the volume will decrease by a factor of 4.