The temperature of the system decreases in an

Options

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

Answer

To solve the question about the decrease in temperature of a system, we need to analyze the four options given: adiabatic compression, isothermal compression, isothermal expansion, and adiabatic expansion.

### Step-by-Step Solution:

1. **Understand the Conditions**:
- **Isothermal Processes**: In isothermal processes (options 2 and 3), the temperature remains constant. Therefore, if the temperature of the system decreases, these options can be eliminated.

2. **Analyze Adiabatic Processes**:
- **Adiabatic Processes**: In adiabatic processes (options 1 and 4), there is no heat exchange with the surroundings (Q = 0). According to the first law of thermodynamics, the change in internal energy (ΔE) is equal to the work done (W) on or by the system:
\[ \Delta E = Q + W \implies \Delta E = W \quad (\text{since } Q = 0) \]

3. **Work Done in Adiabatic Expansion**:
- In adiabatic expansion (option 4), the volume of the system increases. The work done by the system during expansion is given by:
\[ W = -P \Delta V \quad (\text{where } \Delta V > 0) \]
- Since the volume increases, ΔV is positive, which means that W is negative. Therefore, the internal energy change (ΔE) becomes negative:
\[ \Delta E = -P \Delta V < 0 \]

4. **Relate Internal Energy Change to Temperature**:
- The change in internal energy is related to the change in temperature (ΔT) through the specific heat at constant volume (C_v):
\[ \Delta E = C_v \Delta T \]
- Since ΔE is negative, this implies that ΔT is also negative:
\[ \Delta T < 0 \implies \text{Temperature decreases} \]

5. **Conclusion**:
- Therefore, in an adiabatic expansion, the temperature of the system decreases. Thus, the correct answer is option 4: **Adiabatic Expansion**.