Question

In an adiabatic change, the pressure and temperature of a diatomic gas are related as \(\mathrm{P} \propto \mathrm{T}^{\mathrm{c}}\), where c is a constant. The value of c is (consider gas molecules are rigid)

• A. \(\frac{9}{7}\)
• B. \(\frac{7}{2}\)
• C. \(\frac{5}{2}\)
• D. \(\frac{4}{3}\)

Hint:

Combine PV^gamma = constant with the ideal gas law to get P proportional to T^(gamma/(gamma-1)).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For an adiabatic change, \(PV^{\gamma}=\) constant and \(PV=nRT\).

Step 2: Eliminate V
This gives \(P^{1-\gamma}T^{\gamma}=\) constant, so \(P\propto T^{\frac{\gamma}{\gamma-1}}\).

Step 3: Gamma for a rigid diatomic gas
\(\gamma=\dfrac{7}{5}\).

Step 4: Calculation
\(c=\dfrac{7/5}{7/5-1}=\dfrac{7/5}{2/5}=\dfrac{7}{2}\).

Final Answer:
The exponent is \(c=\dfrac{7}{2}\). \[ \boxed{\text{(B) }\dfrac{7}{2}} \]