An adiabatic compression is performed on an ideal gas.The final pressure is equal to 0.560 times the initial pressure and the final volume equals 1.50 times the initial volume.What is the adiabatic constant for the gas?
A) 1.33
B) 1.43
C) 1.48
D) 1.52
E) 1.67

Question

Quizplus · Accepted Answer

The relationship between pressure, volume, and temperature for an adiabatic process is given by $PV^{\gamma}=const$, where $\gamma$ is the adiabatic constant. Using the given information, we can set up the following equation:
$$P_fV_f^{\gamma}=P_iV_i^{\gamma}$$
Substituting in the given ratios of final to initial pressure and volume:
$$0.56 \cdot (1.5V_i)^\gamma = P_iV_i^\gamma$$
Simplifying:
$$0.56 \cdot 1.5^\gamma = 1$$
$$\gamma = \frac{\ln(1/0.56)}{\ln(1.5)} \approx 1.43$$
Therefore, the adiabatic constant for the gas is 1.43, which corresponds to choice (B).

An Adiabatic Compression Is Performed on an Ideal Gas