The temperature of the system decreases in the process of

Options

A. Free expansion
B. Isothermal expansion
C. Isothermal compression
D. Adiabatic expansion

Answer

To solve the question regarding which process results in a decrease in the temperature of a system, we will analyze each option provided.

### Step-by-Step Solution:

1. **Understanding Free Expansion**:
- In free expansion, a gas expands into a vacuum without doing any work and without heat exchange (thermally insulated).
- According to the first law of thermodynamics, the change in internal energy (ΔU) is equal to the heat added (ΔQ) minus the work done (W). Since both ΔQ and W are zero, ΔU = 0.
- If ΔU = 0, it implies that the internal energy and thus the temperature of the gas remains constant.
- **Conclusion**: The temperature does not decrease in free expansion.

2. **Understanding Isothermal Expansion**:
- In isothermal expansion, the temperature of the system is kept constant by allowing heat exchange with the surroundings.
- Since the temperature is constant, it does not decrease.
- **Conclusion**: The temperature does not decrease in isothermal expansion.

3. **Understanding Isothermal Compression**:
- Similar to isothermal expansion, isothermal compression also maintains a constant temperature through heat exchange.
- Again, since the temperature remains constant, it does not decrease.
- **Conclusion**: The temperature does not decrease in isothermal compression.

4. **Understanding Adiabatic Expansion**:
- In adiabatic expansion, the gas expands without heat exchange with the surroundings.
- As the gas expands, it does work on the surroundings, which leads to a decrease in internal energy (ΔU < 0).
- According to the first law of thermodynamics, if there is no heat exchange (ΔQ = 0), then ΔU = -W (where W is positive in expansion).
- Since ΔU is negative, it indicates that the internal energy decreases, which results in a decrease in temperature.
- **Conclusion**: The temperature decreases in adiabatic expansion.

### Final Answer:
The correct option is **Adiabatic Expansion**, as it is the process in which the temperature of the system decreases.

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