Adiabatic expansion of a gas causes

Options

A. Cooling
B. Heating
C. No temperature change
D. Zero work done

Answer

**Step-by-Step Solution:**

1. **Understanding Adiabatic Expansion:**
- In an adiabatic process, there is no heat exchange with the surroundings. This means that the heat transfer (ΔQ) is equal to zero.

2. **Identifying the Process:**
- We consider a gas expanding from an initial state (State 1) to a final state (State 2). During this expansion, the volume of the gas increases (V2 > V1).

3. **Work Done during Expansion:**
- The work done (W) by the gas during expansion is given by the integral of pressure (P) with respect to volume (V), expressed mathematically as:
\[ W = \int P \, dV \]
- Since the volume is increasing (V2 > V1), the change in volume (dV) is positive, which means that the work done by the gas is also positive (W > 0).

4. **Applying the First Law of Thermodynamics:**
- The first law of thermodynamics states:
\[ \Delta Q = \Delta U + W \]
- For an adiabatic process, ΔQ = 0, so we can write:
\[ 0 = \Delta U + W \]
- Rearranging gives:
\[ \Delta U = -W \]
- Since we established that W is positive, it follows that ΔU (the change in internal energy) must be negative (ΔU < 0).

5. **Relating Internal Energy Change to Temperature Change:**
- The internal energy of an ideal gas is directly related to its temperature. A decrease in internal energy (ΔU < 0) implies that the temperature of the gas must also decrease (ΔT < 0).

6. **Conclusion:**
- Since the temperature of the gas decreases during the adiabatic expansion, we conclude that the gas cools down.

**Final Answer:**
- The adiabatic expansion of a gas causes cooling.

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