A diatomic gas with rigid molecules does 10J of work when expanded at constant pressure. The heat energy absorbed by the gas, in this process is ___________ (in J).

Explanation

To solve the problem, we need to determine the heat energy absorbed by a diatomic gas during an isobaric (constant pressure) expansion where the work done is 10 J.

### Step-by-Step Solution:

1. **Identify the Process**:
The problem states that the gas expands at constant pressure, which indicates that this is an isobaric process.

2. **Work Done in Isobaric Process**:
The work done (W) during an isobaric process is given by the formula:
\[ W = P \Delta V \]
However, we also know that for an ideal gas, the work done can be expressed in terms of temperature change:
\[ W = nR \Delta T \]
We are given that \( W = 10 \, \text{J} \).

3. **First Law of Thermodynamics**:
According to the first law of thermodynamics:
\[ Q = \Delta U + W \]
where \( Q \) is the heat absorbed by the gas, \( \Delta U \) is the change in internal energy, and \( W \) is the work done by the gas.

4. **Change in Internal Energy for Diatomic Gas**:
The change in internal energy (\( \Delta U \)) for a diatomic gas can be calculated using the formula:
\[ \Delta U = \frac{f}{2} n R \Delta T \]
where \( f \) is the degrees of freedom. For a diatomic gas, \( f = 5 \).

5. **Relate \( \Delta U \) to Work Done**:
Since we have \( W = nR \Delta T = 10 \, \text{J} \), we can substitute \( nR \Delta T \) into the equation for \( \Delta U \):
\[ \Delta U = \frac{5}{2} \cdot 10 = 25 \, \text{J} \]

6. **Calculate Heat Energy Absorbed**:
Now, substituting \( \Delta U \) and \( W \) into the first law equation:
\[ Q = \Delta U + W = 25 \, \text{J} + 10 \, \text{J} = 35 \, \text{J} \]

### Final Answer:
The heat energy absorbed by the gas is \( \boxed{35 \, \text{J}} \).