Which one of the following statement is true, in respect of the usual quantitates represented by `DeltaQ,DeltaU and DeltaW.`

Options

A. `DeltaU and DeltaW` are path dependent
B. `DeltaQ and DeltaU` are path dependent
C. `DeltaU` does not depends upon path.
D. `DeltaQ ` does not depends upon path

Answer

To determine which statement is true regarding the quantities represented by ΔQ (heat), ΔU (internal energy), and ΔW (work done), we need to analyze the characteristics of these thermodynamic quantities.

### Step-by-Step Solution:

1. **Understanding the Quantities**:
- **ΔQ (Heat)**: This is the amount of thermal energy transferred due to a temperature difference. It is a path-dependent quantity.
- **ΔU (Internal Energy)**: This is the total energy contained within a system. It is a state function, meaning it depends only on the current state of the system and not on how that state was reached.
- **ΔW (Work Done)**: This is the energy transferred when a force is applied over a distance. Like heat, work is also a path-dependent quantity.

2. **Identifying Path Dependence**:
- **Path-Dependent Quantities**: Both ΔQ and ΔW are path-dependent, meaning the amount of heat or work can vary depending on the process taken to change the state of the system.
- **State Function**: ΔU is a state function, which means it is determined solely by the initial and final states of the system, regardless of the path taken.

3. **Evaluating Statements**:
- From the definitions, we can conclude:
- ΔU is not path-dependent (it is a state function).
- ΔQ is path-dependent.
- ΔW is path-dependent.

4. **Conclusion**:
- The true statement regarding these quantities is that ΔU is a state function, while ΔQ and ΔW are path-dependent quantities.

### Final Answer:
The true statement is: **ΔU is a state function, while ΔQ and ΔW are path-dependent quantities.**