Some gas at 300K is enclosed in a container. Now the container is placed on a fast moving train. While the train is in motion, the temperature of the gas

Options

A. rises above 300 K
B. falls below 300 K
C. remains unchanged
D. becomes unsteady

Answer

To solve the problem regarding the behavior of gas temperature when its container is placed on a fast-moving train, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- The gas is initially at a temperature of 300 K.
- The container is placed on a fast-moving train.

2. **Analyzing the Effect of Train Motion**:
- The train moves with a certain velocity (V). However, the gas inside the container is not directly affected by the train's velocity in terms of temperature.

3. **Temperature Dependence**:
- The temperature of a gas is related to the average kinetic energy of its molecules. The formula for the root mean square (RMS) speed of gas molecules is given by:
\[ V_{rm} = \sqrt{\frac{3RT}{m}} \]
- Here, \( R \) is the gas constant, \( T \) is the temperature in Kelvin, and \( m \) is the mass of the gas molecules.

4. **Velocity of the Container**:
- Since the container is moving with the train, its velocity does not change the average kinetic energy of the gas molecules inside it. The gas molecules are still in thermal equilibrium with each other.

5. **Conclusion on Temperature**:
- The temperature of the gas remains unchanged at 300 K while the train is in motion. This is because the temperature of the gas is dependent on the kinetic energy of the gas molecules, which is not affected by the external motion of the container.

### Final Answer:
The temperature of the gas remains at 300 K while the container is on the fast-moving train.

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