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 the 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. Let the initial state be $P_1V_1=nRT_1$, and the final state be $P_2V_2=nRT_2$.

Step2: Analyze the change in pressure

If the pressure is doubled, $P_2 = 2P_1$. From $PV=nRT$, when $T$ is constant ($n$ and $R$ are also constant), we have $P_1V_1=P_2V_{2a}$, substituting $P_2 = 2P_1$ gives $P_1V_1 = 2P_1V_{2a}$, so $V_{2a}=\frac{V_1}{2}$.

Step3: Analyze the change in temperature

Then the temperature is doubled, $T_2 = 2T_1$. Now, with the new - pressure $P_2 = 2P_1$ and new - temperature $T_2 = 2T_1$, from $P_2V_2=nRT_2$, substituting $P_2 = 2P_1$ and $T_2 = 2T_1$ into $P_2V_2=nRT_2$ and $P_1V_1=nRT_1$ gives $2P_1V_2=nR(2T_1)$. Since $P_1V_1=nRT_1$, we can see that $V_2 = V_1$.

Answer:

The volume of the gas would remain the same.