Question

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio \(C_{p}/C_{v}\) for the gas is

• A. \(\frac{4}{3}\)
• B. \(\frac{2}{1}\)
• C. \(\frac{5}{3}\)
• D. \(\frac{3}{2}\)

Hint:

For an adiabatic process, P is proportional to T raised to gamma over gamma minus 1. Equate this power with 3.

Answer 1

The Correct Option is D

Step 1: Formula First
$\dfrac{\gamma}{\gamma-1}=3$ from the adiabatic relation between P and T.

Step 2: Substitution Check
Try $\gamma=\dfrac{3}{2}$: $\dfrac{3/2}{1/2}=3$, which fits.

Step 3: Compare the options
Only option (D), $\dfrac{3}{2}$, satisfies this.

Final Answer:
The value of gamma is 3/2. \[ \boxed{\text{(D) }\dfrac{3}{2}} \]