The relationship between enthalpy change `(DeltaH)` and internal energy change `(DeltaE)` for a system is given by

Options

A. `DeltaH=DeltaE+PDeltaV`
B. `DeltaH=DeltaE-PDeltaV`
C. `DeltaH=DeltaE+PV`
D. `DeltaH=DeltaE+RT`

Answer

To find the relationship between enthalpy change (ΔH) and internal energy change (ΔE) for a system, we can follow these steps:

### Step 1: Understand the Definitions
Enthalpy (H) is defined as:
\[ H = E + PV \]
where:
- \( H \) = Enthalpy
- \( E \) = Internal energy
- \( P \) = Pressure
- \( V \) = Volume

### Step 2: Write the Change in Enthalpy
For a process occurring at constant pressure, the change in enthalpy (ΔH) can be expressed as:
\[ \Delta H = H_2 - H_1 \]

### Step 3: Substitute the Definition of Enthalpy
Using the definition of enthalpy, we can write:
\[ \Delta H = (E_2 + P V_2) - (E_1 + P V_1) \]

### Step 4: Rearrange the Equation
This simplifies to:
\[ \Delta H = (E_2 - E_1) + P (V_2 - V_1) \]
Thus, we can express this as:
\[ \Delta H = \Delta E + P \Delta V \]
where:
- \( \Delta E = E_2 - E_1 \)
- \( \Delta V = V_2 - V_1 \)

### Step 5: Conclusion
The final relationship between the change in enthalpy and the change in internal energy is:
\[ \Delta H = \Delta E + P \Delta V \]