When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by `Delta T`. The heat required to produce the same change in temperature, at a constant pressure is , where xQ is ___________ .

Explanation

To solve the problem, we need to find the heat required to produce the same change in temperature \(\Delta T\) for a diatomic gas at constant pressure, given that the heat \(Q\) is supplied at constant volume.

### Step-by-step Solution:

1. **Understanding Heat at Constant Volume**:
- For a diatomic gas, the molar heat capacity at constant volume (\(C_V\)) is given by:
\[ C_V = \frac{5R}{2} \]
- The heat supplied at constant volume when the temperature increases by \(\Delta T\) is:
\[ Q = N C_V \Delta T \]
- Substituting the value of \(C_V\):
\[ Q = N \left(\frac{5R}{2}\right) \Delta T \]

2. **Finding Heat at Constant Pressure**:
- The molar heat capacity at constant pressure (\(C_P\)) is related to \(C_V\) by the equation:
\[ C_P = C_V + R \]
- Substituting the value of \(C_V\):
\[ C_P = \frac{5R}{2} + R = \frac{7R}{2} \]
- The heat required at constant pressure to produce the same change in temperature \(\Delta T\) is:
\[ Q' = N C_P \Delta T \]
- Substituting the value of \(C_P\):
\[ Q' = N \left(\frac{7R}{2}\right) \Delta T \]

3. **Relating \(Q'\) to \(Q\)**:
- From the equation for \(Q\):
\[ Q = N \left(\frac{5R}{2}\right) \Delta T \]
- We can express \(N \Delta T\) from this equation:
\[ N \Delta T = \frac{2Q}{5R} \]
- Now substituting \(N \Delta T\) into the equation for \(Q'\):
\[ Q' = N \left(\frac{7R}{2}\right) \Delta T = \frac{7R}{2} \cdot \frac{2Q}{5R} \]
- Simplifying this:
\[ Q' = \frac{7 \cdot 2Q}{2 \cdot 5} = \frac{7Q}{5} \]

4. **Final Result**:
- Therefore, the heat required to produce the same change in temperature at constant pressure is:
\[ Q' = \frac{7}{5} Q \]

### Conclusion:
The value of \(xQ\) is \(\frac{7}{5}Q\).