Rankers Physics
Topic: Thermal Physics
Subtopic: Thermodynamics

Which of the following methods will enable the volume of an ideal gas to be made four times ? (Consider absolute temperature)
Quarter the pressure at constant temperature
Quarter the temperature at constant pressure
Half the temperature, double the pressure
Double the temperature, double the pressure

Solution:

To make the volume of an ideal gas four times its initial volume, we can use Boyle's Law, which states:

\[
P \propto \frac{1}{V} \quad \text{(at constant temperature)}
\]

If the initial pressure is \( P \) and the initial volume is \( V \), we want the final volume \( V_{\text{final}} = 4V \).

According to Boyle's Law:

\[
P_{\text{final}} \times V_{\text{final}} = P \times V
\]

Substituting \( V_{\text{final}} = 4V \):

\[
P_{\text{final}} \times 4V = P \times V
\]

\[
P_{\text{final}} = \frac{P}{4}
\]

So, to make the volume four times, we quarter the pressure at constant temperature.

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