An open container is placed in atmosphere. During a time interval, temperature of atmosphere increase and then decreases. The internal energy of gas in container

Options

A. First increases then decreases because internal energy depends upon temperature
B. First decreases then increases
C. Remains constant
D. Is inversely proportional to temperature

Answer

To solve the problem regarding the change in internal energy of a gas in an open container as the temperature of the atmosphere changes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Initial and Final Temperatures**:
- Let the initial temperature of the gas in the container be \( T_0 \).
- The temperature of the atmosphere increases to \( T_1 \) and then decreases back to \( T_0 \).

2. **Calculate Change in Internal Energy During Temperature Increase**:
- When the temperature increases from \( T_0 \) to \( T_1 \), the change in internal energy (\( \Delta U_1 \)) can be calculated using the formula:
\[ \Delta U_1 = n C_v (T_1 - T_0) \]
- Here, \( n \) is the number of moles of the gas and \( C_v \) is the specific heat capacity at constant volume.

3. **Calculate Change in Internal Energy During Temperature Decrease**:
- When the temperature decreases from \( T_1 \) back to \( T_0 \), the change in internal energy (\( \Delta U_2 \)) can be calculated as:
\[ \Delta U_2 = n C_v (T_0 - T_1) \]
- Notice that this is negative since the temperature is decreasing.

4. **Combine the Changes in Internal Energy**:
- The total change in internal energy (\( \Delta U_{\text{net}} \)) over the entire process (increase and then decrease) is given by:
\[ \Delta U_{\text{net}} = \Delta U_1 + \Delta U_2 \]
- Substituting the expressions from the previous steps:
\[ \Delta U_{\text{net}} = n C_v (T_1 - T_0) + n C_v (T_0 - T_1) \]
- Simplifying this gives:
\[ \Delta U_{\text{net}} = n C_v (T_1 - T_0 + T_0 - T_1) = n C_v (0) = 0 \]

5. **Conclusion**:
- The total change in internal energy of the gas in the container is zero. This means that the internal energy of the gas returns to its original state after the temperature fluctuations.

### Final Answer:
The internal energy of the gas in the container remains constant throughout the process, resulting in a total change of zero.

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