The relation between change in internal energy`(DeltaE)`change in enthalpy`(DeltaH)` and work done`(W)`is represented as

Options

A. `DeltaH=DeltaE+W`
B. `W=DeltaE-DeltaH`
C. `DeltaE=W-DeltaH`
D. `DeltaE=DeltaH+W`

Explanation

To find the relation between the change in internal energy (ΔE), change in enthalpy (ΔH), and work done (W), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Internal Energy (U): The total energy contained within a system.
- Enthalpy (H): A thermodynamic quantity defined as H = U + PV, where P is pressure and V is volume.

2. **Write the Relation for Enthalpy**:
- The formula for enthalpy can be expressed as:
\[ H = U + PV \]

3. **Differentiate the Enthalpy Expression**:
- When we take the change in enthalpy (ΔH), we differentiate the equation:
\[ \Delta H = \Delta U + P\Delta V \]

4. **Substitute for Work Done**:
- The work done (W) during a process at constant pressure is given by:
\[ W = P\Delta V \]
- Therefore, we can substitute PΔV in the ΔH equation:
\[ \Delta H = \Delta U + W \]

5. **Relate Internal Energy and Change in Internal Energy**:
- Since the change in internal energy (ΔE) is often denoted as ΔU, we can write:
\[ \Delta H = \Delta E + W \]

6. **Final Relation**:
- Thus, the final relation between change in internal energy, change in enthalpy, and work done is:
\[ \Delta H = \Delta E + W \]

### Conclusion:
The correct relation is:
\[ \Delta H = \Delta E + W \]