Question

A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If \(γ = 1.5\), then the increase in the temperature of the gas in Kelvin is (\(γ\) is the ratio of specific heats)

• A. \(273\)
• B. \(373\)
• C. \(473\)
• D. \(573\)

Hint:

Use T V^(gamma - 1) = constant with normal temperature taken as 273 K.

Answer 1

The Correct Option is A

Step 1: Why Adiabatic:
"Suddenly" means no time for heat exchange, so $Q=0$ and $TV^{\gamma-1}$ stays constant.

Step 2: Compute:
$\dfrac{T_2}{T_1}=4^{1/2}=2$, so the temperature doubles from 273 K to 546 K.

Step 3: Rise:
The increase is $546-273=273$ K. Option (A).

Final Answer:
Option (A). \[ \boxed{\text{(A) } 273} \]