Assertion : In an isothemal expansion the gas absorbs heat and does work .
Reason: In an isothermal process there is no change in internal energy of an ideal gas.

Options

A. Both assertion and reason are true and reason is the correct explanation of assertion
B. Both assertion and reason are true but reason is not the correct explanation of assertion
C. Assertion is true but reason is false
D. Both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that "In an isothermal expansion, the gas absorbs heat and does work."

- In an isothermal process, the temperature of the gas remains constant.
- For an ideal gas undergoing isothermal expansion, the gas absorbs heat (Q) from the surroundings and does work (W) on the surroundings.

### Step 2: Apply the First Law of Thermodynamics
The first law of thermodynamics is given by the equation:
\[ \Delta U = Q - W \]
where:
- \(\Delta U\) is the change in internal energy,
- \(Q\) is the heat added to the system,
- \(W\) is the work done by the system.

### Step 3: Analyze the Reason
The reason states that "In an isothermal process, there is no change in internal energy of an ideal gas."

- For an ideal gas, the internal energy (U) is a function of temperature. Since the temperature remains constant in an isothermal process, the change in internal energy (\(\Delta U\)) is zero:
\[ \Delta U = 0 \]

### Step 4: Substitute into the First Law
Substituting \(\Delta U = 0\) into the first law equation gives:
\[ 0 = Q - W \]
This implies:
\[ Q = W \]
This means that the heat absorbed by the gas is equal to the work done by the gas.

### Step 5: Conclusion
Since both the assertion and reason are true, and the reason correctly explains the assertion, we conclude that:

- **Assertion**: True
- **Reason**: True (and it is the correct explanation for the assertion)

Thus, the correct option is:
**Both assertion and reason are true, and the reason is the correct explanation of the assertion.**