An ideal gas is compressed in a closed container its U

Options

A. Increases
B. Decreases
C. Remains same
D. Both (1) & (2)

Answer

To solve the question regarding the internal energy of an ideal gas being compressed in a closed container, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the System**:
- We have an ideal gas in a closed container that is being compressed. This means that the volume of the gas is decreasing.

2. **Internal Energy of an Ideal Gas**:
- The internal energy (U) of an ideal gas is related to its temperature. For an ideal gas, the change in internal energy (ΔU) can be expressed as:
\[ \Delta U = n C_v \Delta T \]
- Where:
- \( n \) = number of moles of the gas
- \( C_v \) = specific heat capacity at constant volume
- \( \Delta T \) = change in temperature

3. **Effect of Compression on Temperature**:
- When the gas is compressed, work is done on the gas. According to the first law of thermodynamics, when work is done on the gas, the internal energy increases, which typically results in an increase in temperature (ΔT > 0).

4. **Analyzing the Change in Internal Energy**:
- Since the temperature of the gas increases due to compression, and since \( n \) and \( C_v \) are constants for a given amount of gas, we can conclude that:
\[ \Delta U = n C_v \Delta T > 0 \]
- This indicates that the internal energy of the gas increases.

5. **Conclusion**:
- Therefore, the internal energy of the gas increases when it is compressed in a closed container.

### Final Answer:
The internal energy of the gas **increases**.

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