`DeltaE=0` for which process

Options

A. Cyclic process
B. Isothermal expansion
C. Isochoric process
D. Adiabatic process

Explanation

To determine for which processes the change in internal energy (ΔE) is equal to zero, we can analyze different thermodynamic processes based on the first law of thermodynamics.

### Step-by-Step Solution:

1. **Understanding the First Law of Thermodynamics**:
The first law states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W). Mathematically, this is expressed as:
\[ \Delta U = Q - W \]

2. **Isothermal Process**:
In an isothermal process, the temperature of the system remains constant. Since the internal energy of an ideal gas depends only on temperature, if the temperature does not change, the internal energy also does not change. Therefore:
\[ \Delta U = 0 \]
This means that for an isothermal process, ΔE = 0.

3. **Adiabatic Process**:
In an adiabatic process, there is no heat exchange with the surroundings (Q = 0). However, work is done by or on the system. In this case, the internal energy changes according to the work done:
\[ \Delta U = W \]
Thus, ΔE is not equal to zero in an adiabatic process.

4. **Isochoric Process**:
In an isochoric process, the volume of the system remains constant, which means no work is done (W = 0). Therefore, the change in internal energy is equal to the heat added to the system:
\[ \Delta U = Q \]
If no heat is added or removed (Q = 0), then ΔU = 0. However, if heat is added, ΔU will not be zero.

5. **Cyclic Process**:
In a cyclic process, the system returns to its initial state after a series of changes. Since the internal energy is a state function, the change in internal energy over one complete cycle is zero:
\[ \Delta U = 0 \]
Therefore, ΔE = 0 for a cyclic process.

### Conclusion:
The processes for which ΔE = 0 are:
- Isothermal Process
- Cyclic Process