Question

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

• A. \(1.5\)
• B. \(2.5\)
• C. \(3.5\)
• D. \(4.5\)

Hint:

Use T^gamma P^(1-gamma) = constant with gamma = 7/5 for a rigid diatomic gas.

Answer 1

The Correct Option is C

Step 1: Use degrees of freedom:
A rigid diatomic gas has $f=5$, so $\gamma=1+\dfrac2f=\dfrac75$.

Step 2: Substitute into the adiabatic relation:
$TP^{\frac{1-\gamma}{\gamma}}=$ constant, so $P\propto T^{\frac{\gamma}{\gamma-1}}$. Here $\dfrac{\gamma}{\gamma-1}=\dfrac{7/5}{2/5}=3.5$.

Step 3: Pick:
Option C.

Final Answer:
For gamma = 7/5, the exponent gamma/(gamma - 1) is 3.5. \[ \boxed{\text{(C) }3.5} \]