A sample of an ideal gas undergoes on isothermal expansion. If dQ, dU and dW represent the amount of heat supplied, the change in internal energy and the work done respectively,then

Options

A. `dQ = + ve , dU = +ve , dW = +ve`
B. `dQ = + ve, dU = 0, dW = + ve`
C. `dQ = +ve, dU = +ve ,dW = 0`
D. `dQ = -ve, dU = -ve, dW = -ve`

Answer

To solve the problem regarding the isothermal expansion of an ideal gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Process**:
- The gas undergoes isothermal expansion. This means that the temperature (T) of the gas remains constant throughout the process.

2. **Internal Energy Change (dU)**:
- For an ideal gas, the internal energy (U) depends only on the temperature. Since the temperature is constant during an isothermal process, the change in internal energy (dU) is zero.
\[ dU = 0 \]

3. **Work Done (dW)**:
- During expansion, the gas does work on the surroundings. The work done by the gas during an isothermal expansion can be expressed as:
\[ dW = PdV \]
- Since the volume is increasing (expansion), the work done (dW) is positive.

4. **Heat Supplied (dQ)**:
- According to the first law of thermodynamics, we have:
\[ dQ = dU + dW \]
- Substituting the values we found:
\[ dQ = 0 + dW \]
- Therefore, since dW is positive, we conclude that:
\[ dQ = dW > 0 \]
- This indicates that the heat supplied to the system is also positive.

5. **Final Relations**:
- From the above deductions, we can summarize:
- \( dU = 0 \)
- \( dW > 0 \)
- \( dQ > 0 \)

### Conclusion:
The relations for the isothermal expansion of an ideal gas are:
- \( dU = 0 \)
- \( dW > 0 \)
- \( dQ > 0 \)