n moles of an ideal gas with constant volume heat capacity `C_V` undergo an isobaric expansion by certain volume.The ratio of the work done in the process, to the heat supplied is :

Options

A. `(nR)/(C_(V)+nR)`
B. `(nR)/(C_(V)-nR)`
C. `(4nR)/(C_(V)-nR)`
D. `(4nR)/(C_(V)+nR)`

Answer

To solve the problem, we need to find the ratio of the work done (W) during an isobaric expansion of an ideal gas to the heat supplied (H) during the same process.

### Step-by-step Solution:

1. **Understand the Process**:
- We are dealing with an isobaric (constant pressure) expansion of an ideal gas.

2. **Work Done in Isobaric Process**:
- The work done (W) during an isobaric process is given by the formula:
\[ W = nR\Delta T \]
where:
- \( n \) = number of moles of the gas,
- \( R \) = universal gas constant,
- \( \Delta T \) = change in temperature.

3. **Heat Supplied in Isobaric Process**:
- The heat supplied (H) during an isobaric process can be expressed as:
\[ H = C_V \Delta T + W \]
Since we already have the expression for work done, we can substitute it:
\[ H = C_V \Delta T + nR\Delta T \]
This can be simplified to:
\[ H = (C_V + nR)\Delta T \]

4. **Calculate the Ratio**:
- Now, we need to find the ratio of work done to heat supplied:
\[ \frac{W}{H} = \frac{nR\Delta T}{(C_V + nR)\Delta T} \]
- The \(\Delta T\) terms cancel out:
\[ \frac{W}{H} = \frac{nR}{C_V + nR} \]

5. **Final Result**:
- Thus, the ratio of the work done in the process to the heat supplied is:
\[ \frac{W}{H} = \frac{nR}{C_V + nR} \]