Question

12 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? a if the pressure were doubled, the volume would decrease by half; if the temperature were doubled the volume would double. b if the pressure were doubled, the volume would increase by half; if the temperature were doubled the volume would double.

Explanation:

Step1: Recall ideal - gas law

The ideal - gas law is $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the amount of gas, $R$ is the ideal - gas constant, and $T$ is the absolute temperature. Assume $n$ is constant. We can rewrite it as $V=\frac{nR}{P}T$.

Step2: Analyze the effect of pressure change

If the initial state is $V_1=\frac{nR}{P_1}T_1$ and the pressure is doubled ($P_2 = 2P_1$) while temperature remains the same ($T_2=T_1$), then $V_2=\frac{nR}{P_2}T_2=\frac{nR}{2P_1}T_1=\frac{1}{2}\times\frac{nR}{P_1}T_1=\frac{1}{2}V_1$. So when pressure is doubled, volume decreases by half.

Step3: Analyze the effect of temperature change

Now, if we start from the state after pressure change and then double the temperature. Let the new state be $V_3$, with $P_3 = 2P_1$ and $T_3 = 2T_1$. Then $V_3=\frac{nR}{P_3}T_3=\frac{nR}{2P_1}\times2T_1=\frac{nR}{P_1}T_1 = V_1$. When we double the temperature from the state where pressure is already doubled, the volume doubles from the volume after pressure - doubling.

Answer:

A. If the pressure were doubled, the volume would decrease by half; if the temperature were doubled the volume would double.