Pressure in a gas is reduced by half, and the temperature is reduced to 80% of its initial value. What is the ratio of the final to the initial volume of the gas?

Question

Quizplus · Accepted Answer

Using the combined gas law, $ \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} $, where $ P_1 $ and $ P_2 $ are the initial and final pressures, $ V_1 $ and $ V_2 $ are the initial and final volumes, and $ T_1 $ and $ T_2 $ are the initial and final temperatures. Given $ P_2 = \frac{1}{2}P_1 $ and $ T_2 = 0.8T_1 $, substituting these into the equation gives $ \frac{P_1V_1}{T_1} = \frac{\frac{1}{2}P_1V_2}{0.8T_1} $. Simplifying, $ V_2 = 1.6V_1 $, so the ratio of the final to the initial volume is 1.60.

Pressure in a Gas Is Reduced by Half, and the Temperature