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 given 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.

1. **Understanding Heat Addition:** When heat is added to a system, it can lead to an increase in temperature. However, this is not always the case.
2. **Isothermal Process:** In an isothermal process, the temperature of the system remains constant despite the addition of heat. This is because the heat added is used to do work on the surroundings rather than increasing the internal energy of the system.
3. **Conclusion for Statement A:** Since there are processes (like isothermal) where adding heat does not increase temperature, Statement A 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.

1. **Understanding Work Done:** In thermodynamics, work done by a system is defined as \( dW = P dV \), where \( P \) is the pressure and \( dV \) is the change in volume.
2. **Positive Work:** If the work done \( dW \) is positive, it implies that the system is doing work on the surroundings. For this to happen, the volume of the system must increase (i.e., \( dV > 0 \)).
3. **Conclusion for Statement B:** Therefore, if positive work is done by the system, the volume must indeed increase, making Statement B **true**.

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

Thus, the correct answer is that Statement A is incorrect and Statement B is correct.