Question

A diatomic gas undergoes adiabatic change. Its pressure \( P \) and temperature \( T \) are related as \( P \propto T^x \), where \( x \) is

• A. 3.0
• B. 2.5
• C. 3.5
• D. 1.5

Hint:

In an adiabatic process for a diatomic gas, the relationship between pressure and temperature follows \( P \propto T^{\gamma} \), where \( \gamma = 1.4 \).

Answer 1

The Correct Option is A

Step 1: Understanding the adiabatic process.
For an adiabatic process, the relationship between pressure and temperature for a diatomic gas is given by: \[ P \propto T^{\gamma} \] where \( \gamma \) is the adiabatic index, which is \( \gamma = \frac{C_p}{C_v} \), and for a diatomic gas, \( \gamma = 1.4 \).
Step 2: Conclusion.
The value of \( x \) in the equation \( P \propto T^x \) for a diatomic gas undergoing adiabatic change is \( x = 3.0 \), so the correct answer is (A).