When gas in a vessel expands, it internal energy decreases. The process involved is

Options

A. Isobaric
B. Isochoric
C. Isothermal
D. Adiabatic

Answer

To determine the process involved when the internal energy of a gas decreases during expansion, we can analyze the situation step by step using the first law of thermodynamics.

### Step-by-Step Solution:

1. **Understanding the First Law of Thermodynamics**:
The first law states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W):
\[ Q = ΔU + W \]

2. **Identifying the Signs**:
- Since the gas is expanding, the work done by the gas (W) is positive.
- It is given that the internal energy (ΔU) of the gas is decreasing, which means ΔU is negative.

3. **Substituting the Values**:
From the first law, we can rearrange it to find Q:
\[ Q = ΔU + W \]
Since ΔU is negative and W is positive, we can substitute these values:
\[ Q = \text{(negative)} + \text{(positive)} \]
This indicates that the heat added to the system (Q) could be negative, meaning heat is leaving the system.

4. **Analyzing the Process Options**:
- **Isobaric Process**: In an isobaric process, the heat added is given by \( Q = nC_pΔT \). If ΔT is negative (temperature decreases), then Q would also be negative. However, since the work done is positive and the internal energy is decreasing, this option does not satisfy all conditions.
- **Isochoric Process**: In an isochoric process, the volume remains constant, so there is no expansion work done (W = 0). This contradicts the condition that the gas is expanding.
- **Isothermal Process**: In an isothermal process, the temperature remains constant, which means the internal energy does not change (ΔU = 0). This contradicts the condition that ΔU is negative.
- **Adiabatic Process**: In an adiabatic process, there is no heat exchange with the surroundings (Q = 0). Thus, from the first law:
\[ ΔU = -W \]
Since W is positive (work done by the gas), ΔU must be negative. This satisfies the condition that the internal energy decreases while the gas expands.

5. **Conclusion**:
The only process that satisfies the conditions of the problem (internal energy decreases while the gas expands) is the **adiabatic process**.

### Final Answer:
The process involved is **adiabatic**.