An ideal gas is compressed in a closed container its U

Options

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

Explanation

To solve the problem regarding the change in internal energy (U) of an ideal gas when it is compressed in a closed container, we can follow these steps:

### Step 1: Understand the Internal Energy of an Ideal Gas
The internal energy (U) of an ideal gas is given by the formula:
\[ U = n C_v \Delta T \]
where:
- \( n \) = number of moles of the gas
- \( C_v \) = specific heat capacity at constant volume
- \( \Delta T \) = change in temperature

### Step 2: Analyze the Compression of the Gas
When an ideal gas is compressed in a closed container, the volume of the gas decreases. According to the ideal gas law, if the volume decreases while the number of moles remains constant, the pressure and temperature of the gas will change.

### Step 3: Determine the Effect on Temperature
In a closed container, compressing the gas will typically lead to an increase in temperature. This is because work is done on the gas during compression, which increases its internal energy and, consequently, its temperature.

### Step 4: Relate Temperature Change to Internal Energy
Since the internal energy is directly proportional to the change in temperature (\( \Delta T \)), if the temperature increases due to compression, the internal energy must also increase. Thus, we can conclude:
\[ \Delta T > 0 \Rightarrow U \text{ increases} \]

### Step 5: Conclusion
Based on the analysis, when the ideal gas is compressed in a closed container, its internal energy (U) increases.

### Final Answer
The correct answer is that the internal energy (U) of the ideal gas **increases**.

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