Question

A rigid diatomic gas having molar mass m is contained in an insulated container. The container is moving with velocity V. If it is stopped suddenly, the change in temperature is (R - gas constant)

• A. \(\frac{mV^2}{R}\)
• B. \(\frac{mV^2}{3R}\)
• C. \(\frac{mV^2}{5R}\)
• D. \(\frac{mV^2}{7R}\)

Hint:

The kinetic energy of the bulk motion becomes internal energy; use Cv = 5R/2.

Answer 1

The Correct Option is C

Step 1: Energy conversion
Let the gas be \(n\) moles with molar mass \(m\), so its mass is \(nm\). The bulk kinetic energy is \(\frac12nmV^2\).

Step 2: Internal energy gain
A rigid diatomic gas has \(C_v = \frac52R\). The container is insulated, so all energy goes into heating: \(nC_v\Delta T = \frac12nmV^2\).

Step 3: Solve
\[ \Delta T = \frac{mV^2}{2C_v} = \frac{mV^2}{5R} \]
Option (C).

Final Answer:
The temperature change is mV^2/(5R). \[ \boxed{\text{(C)}\ \Delta T=\frac{mV^2}{5R}} \]