A : Heat supplied to a gaseous system in an isothermal process is used to do work against surroundings.
R : During isothermal process there is no change ininternal energy of the system.

Options

A. If both Assertion & Reason are true and the reason is the correct explantion of the assertion, then mark(1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the question, we need to analyze the assertion (A) and the reason (R) provided in the context of thermodynamics, specifically focusing on the isothermal process.

### Step-by-Step Solution:

1. **Understanding the Isothermal Process**:
- An isothermal process is a thermodynamic process in which the temperature of the system remains constant (ΔT = 0).

2. **First Law of Thermodynamics**:
- The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W):
\[ \Delta U = Q - W \]

3. **Applying the Isothermal Condition**:
- In an isothermal process, since the temperature is constant, the change in internal energy (ΔU) is zero:
\[ \Delta U = 0 \]
- Substituting this into the first law equation gives:
\[ 0 = Q - W \implies Q = W \]
- This means that all the heat supplied to the system is converted into work done by the system.

4. **Interpreting the Assertion (A)**:
- The assertion states that "Heat supplied to a gaseous system in an isothermal process is used to do work against surroundings."
- Since we derived that Q = W in an isothermal process, the assertion is correct.

5. **Interpreting the Reason (R)**:
- The reason states that "During isothermal process there is no change in internal energy of the system."
- This is also correct because we established that ΔU = 0 in an isothermal process.

6. **Conclusion**:
- Both the assertion (A) and the reason (R) are correct, and the reason correctly explains the assertion.

### Final Answer:
Both A and R are correct, and R is the correct explanation for A.

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