In a isobaric process the work done by a di-atomic gas is 10 J , the heat given to the gas will be :

Options

A. 35 J
B. 30 J
C. 45 J
D. 60 J

Explanation

To solve the problem, we need to find the heat given to a diatomic gas during an isobaric process when the work done by the gas is 10 J.

### Step-by-Step Solution:

1. **Understand the Isobaric Process**:
In an isobaric process, the pressure remains constant. The work done (W) by the gas can be expressed as:
\[ W = n \cdot R \cdot T \]
where \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is the temperature.

2. **Heat in an Isobaric Process**:
The heat (Q) added to the gas at constant pressure is given by:
\[ Q = n \cdot C_p \cdot \Delta T \]
where \( C_p \) is the specific heat at constant pressure.

3. **Relate Work Done and Heat**:
From thermodynamic principles, we can relate the work done and heat added in an isobaric process:
\[ \frac{W}{Q} = \frac{R}{C_p} \]
Rearranging this gives us:
\[ Q = \frac{W \cdot C_p}{R} \]

4. **Determine \( C_p \) for a Diatomic Gas**:
For a diatomic gas, the degrees of freedom (f) is 5. The specific heat at constant pressure can be expressed as:
\[ C_p = \frac{f + 2}{2} R = \frac{5 + 2}{2} R = \frac{7}{2} R \]

5. **Substituting \( C_p \) into the Heat Equation**:
Substitute \( C_p \) into the equation for Q:
\[ Q = \frac{W \cdot \left(\frac{7}{2} R\right)}{R} \]
The \( R \) cancels out:
\[ Q = W \cdot \frac{7}{2} \]

6. **Calculate Heat (Q)**:
Given that \( W = 10 \, J \):
\[ Q = 10 \cdot \frac{7}{2} = 10 \cdot 3.5 = 35 \, J \]

### Final Answer:
The heat given to the gas is \( Q = 35 \, J \).

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