Question

A rigid diatomic ideal gas is compressed adiabatically to \((1/32)\) of its initial volume. If the initial temperature of the gas is \(T_{1}\) (in kelvin) and the final temperature is "\(nT_{1}\)", the value of n is \(\{\gamma =1.4\}\)

• A. \(1\)
• B. \(2\)
• C. \(3\)
• D. \(4\)

Hint:

Use T V^(gamma-1) = constant with the given volume ratio and gamma = 1.4.

Answer 1

The Correct Option is D

Step 1: Formula-first approach
Use $\dfrac{T_2}{T_1}=\left(\dfrac{V_1}{V_2}\right)^{\gamma-1}$.

Step 2: Substitute
$\dfrac{T_2}{T_1}=32^{0.4}=(2^{5})^{2/5}$

Step 3: Simplify
This equals $2^{2}=4$, so $n=4$, option (D).

Final Answer:
The final temperature is $4T_1$, so n is 4. \[ \boxed{\text{(D) }4} \]