How does internal energy of a gas change in (i) isothermal expansion (ii) adiabatic expansion?

Explanation

To understand how the internal energy of a gas changes during isothermal and adiabatic expansions, we can break it down into two parts:

### Step 1: Isothermal Expansion
1. **Definition**: In an isothermal process, the temperature of the gas remains constant.
2. **Change in Temperature**: Since the temperature is constant, the change in temperature (dT) is zero.
3. **Relation to Internal Energy**: The internal energy (U) of an ideal gas is directly proportional to its temperature (U ∝ T). Therefore, if there is no change in temperature, there will be no change in internal energy.
4. **Conclusion**: Thus, during isothermal expansion, the internal energy of the gas remains constant (ΔU = 0).

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