Answer to Question #208606 in Physics for Anonn

Question

The pressure of an ideal gas is reduced by 50%, resulting in a decrease in temperature to 75% of the initial value. Calculate the ratio of the final to initial volumes of the gas. 

Answer 1

Initial pressure: $P_0$

Final pressure: $P_1=0.5P_0$

Initial temperature: $T_0$

Final temperature: $T_1=1.75T_0$

According to the combined gas law:

$$\frac{P_0V_0}{T_0}=\frac{P_1V_1}{T_1},\\\space\\ \frac{V_1}{V_0}=\frac{T_1P_0}{T_0P_1}=\frac{1.75·1}{1·0.5}=3.5.$$