Given below are two statements : ,br> Statement `I`: If heat is added to a system , its tempearture must increase.
Statement `II` : If positive work is done by a system in a thermodynamic process, its volume must increase.
In the light of the above statement, choose the correct answer from the options given below

Options

A. Both Statement `I` and statement `II` are false
B. Statement `I` is false but statement `II` is true
C. Both Statement `I` and statement `II` are true
D. Statement `I` is true but statement `II` is false

Answer

To solve the problem, we need to analyze both statements given in the question.

**Step 1: Analyze Statement I**
- Statement I claims: "If heat is added to a system, its temperature must increase."
- In thermodynamics, when heat is added to a system, the effect on temperature depends on the type of process the system undergoes. For example, in an isothermal process (where the temperature remains constant), heat can be added without changing the temperature. Therefore, it is not necessarily true that adding heat will always increase the temperature.
- **Conclusion**: Statement I is **false**.

**Step 2: Analyze Statement II**
- Statement II claims: "If positive work is done by a system in a thermodynamic process, its volume must increase."
- In thermodynamics, the work done by a system is defined as \( W = P \Delta V \), where \( P \) is the pressure and \( \Delta V \) is the change in volume. If the work done is positive (i.e., the system is doing work on the surroundings), it implies that the volume of the system must increase (\( \Delta V > 0 \)).
- **Conclusion**: Statement II is **true**.

**Step 3: Final Conclusion**
- Given the analysis, we conclude that Statement I is false and Statement II is true. Therefore, the correct answer is that Statement I is false and Statement II is true.

### Summary of the Solution:
- Statement I: False
- Statement II: True
- Correct option: Statement I is false and Statement II is true.