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 both the assertion (A) and the reason (R) provided.

### Step 1: Understand the Assertion
The assertion states that "Heat supplied to a gaseous system in an isothermal process is used to do work against surroundings." In an isothermal process, the temperature of the system remains constant.

### Step 2: Understand the Reason
The reason states that "During isothermal process there is no change in internal energy of the system." For an ideal gas, the internal energy (U) depends solely on temperature. Since the temperature does not change in an isothermal process, the internal energy also remains constant.

### Step 3: Apply the First Law of Thermodynamics
According to the First Law of Thermodynamics:
\[ \Delta Q = \Delta U + \Delta W \]
Where:
- \(\Delta Q\) is the heat added to the system,
- \(\Delta U\) is the change in internal energy,
- \(\Delta W\) is the work done by the system.

### Step 4: Analyze the Isothermal Process
Since the process is isothermal, we have:
- \(\Delta T = 0\) (no change in temperature),
- Therefore, \(\Delta U = 0\) (no change in internal energy).

Substituting these values into the First Law equation gives:
\[ \Delta Q = 0 + \Delta W \]
This simplifies to:
\[ \Delta Q = \Delta W \]
This means that all the heat supplied to the system is converted into work done by the system against the surroundings.

### Step 5: Conclusion
Both the assertion and the reason are correct. The reason correctly explains why the assertion is true. Therefore, the answer is that both the assertion and the reason are true, and the reason is the correct explanation of the assertion.

### Final Answer
Both assertion and reason are correct, and the reason is the correct explanation of the assertion.