Which of the following is/are independent of path?

Options

A. Adiabatic work
B. Isobaric heat
C. Isothermal work
D. Change in enthalpy

Explanation

To determine which of the given options are independent of the path, we need to identify which of them are state functions. State functions are properties that depend only on the initial and final states of a system, not on the path taken to get from one state to another.

Let's analyze each option step by step:

### Step 1: Analyze Adiabatic Work
- **Definition**: Adiabatic work occurs when no heat is exchanged with the surroundings (Q = 0).
- **Relation**: The change in internal energy (ΔU) is given by ΔU = Q + W. Since Q = 0, we have ΔU = W.
- **Conclusion**: Since ΔU is a state function (it depends only on the initial and final states), adiabatic work (W) is also a state function.
- **Path Independence**: **Adiabatic work is independent of the path.**

### Step 2: Analyze Isobaric Heat
- **Definition**: Isobaric heat refers to the heat exchanged at constant pressure, represented as Qp.
- **Relation**: Qp is given by Qp = CpΔT, where Cp is the heat capacity at constant pressure and ΔT is the change in temperature.
- **Conclusion**: Since Qp depends on the initial and final temperatures, it is a state function.
- **Path Independence**: **Isobaric heat is independent of the path.**

### Step 3: Analyze Isothermal Work
- **Definition**: Isothermal work occurs at constant temperature.
- **Relation**: The work done in an isothermal process depends on the specific path taken (e.g., the volume change).
- **Conclusion**: Since isothermal work depends on the path taken to achieve the change in state, it is not a state function.
- **Path Independence**: **Isothermal work is dependent on the path.**

### Step 4: Analyze Change in Enthalpy
- **Definition**: Change in enthalpy (ΔH) is the heat content change at constant pressure.
- **Relation**: ΔH is defined as ΔH = ΔU + PΔV, and it depends only on the initial and final states of the system.
- **Conclusion**: Since ΔH is a state function, it is independent of the path taken.
- **Path Independence**: **Change in enthalpy is independent of the path.**

### Final Conclusion
Based on the analysis:
- **Options that are independent of the path**:
- Adiabatic work (Option 1)
- Isobaric heat (Option 2)
- Change in enthalpy (Option 4)
- **Option that is dependent on the path**:
- Isothermal work (Option 3)

### Summary of Results
- **Independent of Path**: Options 1, 2, and 4.
- **Dependent on Path**: Option 3.