consider the following two statements.
(A) If heat is added to a system, its temperature must increase.
(b) if positive work is done by a system in a thermodynamic process, its volume must increase.

Options

A. both A and B are correct.
B. A is correct but B is wrong.
C. B is correct but A is wrong.
D. Both A and B are wrong.

Explanation

To analyze the two statements provided in the question, we will evaluate each statement one by one.

### Step 1: Evaluate Statement A
**Statement A:** If heat is added to a system, its temperature must increase.

- **Analysis:** This statement is not necessarily true. The temperature of a system can remain constant even when heat is added, particularly in an isothermal process. In an isothermal process, the system absorbs heat, but the temperature does not change because the heat is used to do work or to change the phase of the substance (e.g., melting or boiling). Therefore, it is possible for heat to be added without an increase in temperature.

**Conclusion for Statement A:** This statement is **false**.

### Step 2: Evaluate Statement B
**Statement B:** If positive work is done by a system in a thermodynamic process, its volume must increase.

- **Analysis:** In thermodynamics, work done by a system is defined as the product of pressure and the change in volume (W = P * ΔV). If positive work is done, it implies that the system is expanding against an external pressure. For the work to be positive, the change in volume (ΔV) must be positive, which means the final volume is greater than the initial volume. Thus, if positive work is done, the volume of the system must indeed increase.

**Conclusion for Statement B:** This statement is **true**.

### Final Conclusion
- **Statement A is false.**
- **Statement B is true.**

Thus, the correct option is that **A is incorrect and B is correct**.

### Answer:
**Option 3: B is correct and A is wrong.**

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