In an isothermal expansion change in internal energy and work done by the gas are respectively

Options

A. (-)ve, (-) ye
B. 0, (+)ve
C. 0,(-)ve
D. (+) ve, (-) ve

Explanation

To solve the question regarding the change in internal energy and work done by the gas during an isothermal expansion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Isothermal Process**:
- An isothermal process is one that occurs at a constant temperature. In such a process, the internal energy of an ideal gas depends only on its temperature.

2. **Change in Internal Energy**:
- The formula for the change in internal energy (ΔU) for an ideal gas is given by:
\[ \Delta U = n C_v \Delta T \]
where:
- \( n \) = number of moles of gas
- \( C_v \) = molar heat capacity at constant volume
- \( \Delta T \) = change in temperature
- Since the process is isothermal, the temperature does not change (\( \Delta T = 0 \)). Therefore:
\[ \Delta U = n C_v \cdot 0 = 0 \]

3. **Work Done by the Gas**:
- In an isothermal expansion, the work done (W) by the gas can be calculated using the formula:
\[ W = nRT \ln\left(\frac{V_f}{V_i}\right) \]
where:
- \( R \) = universal gas constant
- \( T \) = absolute temperature (constant during isothermal process)
- \( V_f \) = final volume
- \( V_i \) = initial volume
- Since the gas is expanding, \( V_f > V_i \), which implies that \( W > 0 \) (work done by the gas is positive).

4. **Conclusion**:
- Therefore, in an isothermal expansion:
- The change in internal energy (ΔU) is **0**.
- The work done by the gas (W) is a **positive quantity**.

### Final Answer:
- Change in internal energy (ΔU) = 0
- Work done by the gas (W) = Positive quantity