Which of the following can be zero for isothermal reversible expansion?

Options

A. `Delta E`
B. `Delta H`
C. `Delta T`
D. All of these

Answer

To solve the question "Which of the following can be zero for isothermal reversible expansion?", we need to analyze the conditions of an isothermal reversible expansion process in thermodynamics.

### Step-by-Step Solution:

1. **Understanding Isothermal Process**:
- An isothermal process occurs at a constant temperature. Therefore, the change in temperature (ΔT) is zero.
- **Hint**: Remember that in an isothermal process, the temperature does not change.

2. **Analyzing Reversible Process**:
- A reversible process is one that can be reversed without leaving any change in the system and surroundings. It occurs infinitely slowly, ensuring that the system is in equilibrium at all times.
- **Hint**: Reversible processes are characterized by equilibrium at every stage.

3. **Identifying Relevant Thermodynamic Quantities**:
- In thermodynamics, we often deal with changes in internal energy (ΔE), enthalpy (ΔH), and other state functions. For an ideal gas undergoing an isothermal process, the change in internal energy (ΔE) is directly related to temperature.
- **Hint**: For an ideal gas, ΔE = 0 when the temperature is constant.

4. **Applying the First Law of Thermodynamics**:
- The first law states that the change in internal energy (ΔE) is equal to the heat added to the system (Q) minus the work done by the system (W).
- For an isothermal process involving an ideal gas, since ΔT = 0, it follows that ΔE = 0.
- **Hint**: Recall that for an ideal gas, internal energy depends only on temperature.

5. **Considering Enthalpy Change (ΔH)**:
- The enthalpy change (ΔH) for an isothermal process can also be expressed as ΔH = nCpΔT. Since ΔT = 0, this implies that ΔH = 0.
- **Hint**: Enthalpy change is related to temperature change; if there is no temperature change, there is no enthalpy change.

6. **Conclusion**:
- For an isothermal reversible expansion, both the change in internal energy (ΔE) and the change in enthalpy (ΔH) can be zero. Thus, the answer to the question is that ΔE and ΔH can be zero.

### Final Answer:
- ΔE (change in internal energy) = 0
- ΔH (change in enthalpy) = 0