Question

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio of \( \frac{C_p}{C_v} \) for the gas is

• A. 3/2
• B. 5/3
• C. 4/3
• D. 2

Hint:

In an adiabatic process, the relationship between pressure and temperature dictates the ratio of specific heats \(C_p\) and \(C_v\), which is determined by the nature of the gas.

Answer 1

The Correct Option is A

For an adiabatic process, the equation for pressure and temperature of an ideal gas is given by: \[ P \propto T^n \] where \(n\) is the adiabatic index. Given that pressure is proportional to the cube of temperature, we have \(n = 3\). For an ideal gas, the ratio \( \frac{C_p}{C_v} \) is related to the adiabatic index \( \gamma \) as: \[ \gamma = \frac{C_p}{C_v} \] From thermodynamics, for a monatomic ideal gas undergoing an adiabatic process, the ratio \( \gamma = 3/2 \). Hence, the correct answer is (a).