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 internal energy of a gas in an open container during a temperature change in the atmosphere, we can follow these steps:

### Step-by-Step Solution:

1. **Define Initial Conditions**:
- Let the initial temperature of the gas in the container be \( T_0 \).

2. **Temperature Increase**:
- The temperature of the atmosphere increases to \( T_1 \).
- The change in internal energy of the gas during this increase can be expressed as:
\[ \Delta U_1 = N \cdot C_v \cdot (T_1 - T_0) \]
- Here, \( N \) is the number of moles of gas and \( C_v \) is the molar heat capacity at constant volume.

3. **Temperature Decrease**:
- After reaching \( T_1 \), the temperature of the atmosphere then decreases back to \( T_0 \).
- The change in internal energy during this decrease is given by:
\[ \Delta U_2 = N \cdot C_v \cdot (T_0 - T_1) \]

4. **Net Change in Internal Energy**:
- To find the total change in internal energy, we sum the changes from both processes:
\[ \Delta U_{\text{net}} = \Delta U_1 + \Delta U_2 \]
- Substituting the expressions from steps 2 and 3:
\[ \Delta U_{\text{net}} = N \cdot C_v \cdot (T_1 - T_0) + N \cdot C_v \cdot (T_0 - T_1) \]
- This simplifies to:
\[ \Delta U_{\text{net}} = N \cdot C_v \cdot (T_1 - T_0 + T_0 - T_1) = N \cdot C_v \cdot 0 = 0 \]

5. **Conclusion**:
- The net change in internal energy of the gas in the container is zero:
\[ \Delta U_{\text{net}} = 0 \]
- This indicates that the internal energy of the gas remains constant throughout the process, despite the changes in temperature of the atmosphere.