A sample of ideal gas `(gamma=1.4)` is heated at constant pressure. If an amount of 100 J heat is supplied to the gas, the work done by the gas is a) 28.57 J b) 56.54 J c) 38. 92 J d) 65.38 J

Options

A. 28.57 J
B. 56.54 J
C. 38.92 J
D. 65.38 J

Explanation

To solve the problem, we need to find the work done by the gas when it is heated at constant pressure. We will use the first law of thermodynamics and the properties of ideal gases.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Heat supplied to the gas, \( Q = 100 \, \text{J} \)
- Heat capacity ratio, \( \gamma = 1.4 \)

2. **Use the First Law of Thermodynamics:**
The first law of thermodynamics states:
\[ Q = W + \Delta U \]
where \( Q \) is the heat added to the system, \( W \) is the work done by the system, and \( \Delta U \) is the change in internal energy.

3. **Relate Change in Internal Energy to Heat:**
For an ideal gas, the change in internal energy can be expressed as:
\[ \Delta U = \frac{Q}{\gamma} \]
Substituting the value of \( Q \):
\[ \Delta U = \frac{100 \, \text{J}}{1.4} \approx 71.43 \, \text{J} \]

4. **Substitute \( \Delta U \) Back into the First Law Equation:**
Rearranging the first law equation gives us:
\[ W = Q - \Delta U \]
Substituting the values we have:
\[ W = 100 \, \text{J} - 71.43 \, \text{J} \approx 28.57 \, \text{J} \]

5. **Final Answer:**
Therefore, the work done by the gas is approximately:
\[ W \approx 28.57 \, \text{J} \]

### Conclusion:
The correct answer is **a) 28.57 J**.