The pressure of a mass of air at 20°C is halved adiabatically. If the ratio of C_p to C_v for air is 1.41, calculate the resulting volume.

Question

Quizplus · Accepted Answer

According to adiabatic process formula, $P_1V_1^{\gamma}=P_2V_2^{\gamma}$ where $\gamma=\frac{C_p}{C_v}$ for the air is 1.41.
If the pressure is halved, then the new pressure becomes $\frac{1}{2}P_1$. The formula becomes: 
$$\frac{1}{2}P_1V_1^{\gamma} = P_1 (\frac{V_2}{V_1})^{\gamma} V_2^{\gamma}$$

simplifies to: $$\frac{1}{2} = (\frac{V_2}{V_1})^{\gamma}$$

$$V_2 = V_1(\frac{1}{2})^{\frac{1}{\gamma}}$$

$$V_2 = V_1(\frac{1}{2})^{\frac{1}{1.41}}$$

$$V_2 = 1.63 V_1$$

Therefore, the resulting volume is 1.63 times the original volume. The correct answer is B.

The Pressure of a Mass of Air at 20°C Is