In an isobaric process of an ideal gas. The ratio of heat supplied annd work done by the system `[i.e.,((Q)/(W))]` is

Options

A. `(gamma-1)/(gamma)`
B. `gamma`
C. `(gamma)/(gamma-1)`
D. `1`

Explanation

To solve the problem, we need to find the ratio of heat supplied (Q) to the work done (W) in an isobaric process for an ideal gas. Let's break it down step by step.

### Step 1: Understand the Isobaric Process
In an isobaric process, the pressure (P) remains constant.

### Step 2: Write the Expression for Heat Supplied (Q)
For an ideal gas undergoing an isobaric process, the heat supplied (Q) can be expressed as:
\[ Q = n C_p \Delta T \]
where:
- \( n \) = number of moles of the gas
- \( C_p \) = molar specific heat capacity at constant pressure
- \( \Delta T \) = change in temperature

### Step 3: Write the Expression for Work Done (W)
The work done (W) by the gas during an isobaric process is given by:
\[ W = P \Delta V \]
Using the ideal gas law, we can express this as:
\[ W = n R \Delta T \]
where:
- \( R \) = universal gas constant

### Step 4: Find the Ratio \( \frac{Q}{W} \)
Now, we can find the ratio of heat supplied to work done:
\[ \frac{Q}{W} = \frac{n C_p \Delta T}{n R \Delta T} \]
Here, \( n \) and \( \Delta T \) cancel out:
\[ \frac{Q}{W} = \frac{C_p}{R} \]

### Step 5: Relate \( C_p \) and \( C_v \) Using \( \gamma \)
We know that:
\[ C_p - C_v = R \]
and the ratio of specific heats is defined as:
\[ \gamma = \frac{C_p}{C_v} \]
From this, we can express \( C_p \) in terms of \( \gamma \) and \( C_v \):
\[ C_p = \gamma C_v \]
Substituting \( C_v = C_p - R \) into the equation gives:
\[ C_p = \gamma (C_p - R) \]
Rearranging this, we find:
\[ C_p (1 - \gamma) = -\gamma R \]
Thus:
\[ C_p = \frac{R \gamma}{\gamma - 1} \]

### Step 6: Substitute \( C_p \) Back into the Ratio
Now substituting \( C_p \) back into our ratio:
\[ \frac{Q}{W} = \frac{C_p}{R} = \frac{\frac{R \gamma}{\gamma - 1}}{R} \]
The \( R \) cancels out:
\[ \frac{Q}{W} = \frac{\gamma}{\gamma - 1} \]

### Conclusion
Thus, the ratio of heat supplied to work done in an isobaric process is:
\[ \frac{Q}{W} = \frac{\gamma}{\gamma - 1} \]

### Final Answer
The correct option is \( \frac{\gamma}{\gamma - 1} \).