Introduction:
In order to calculate the fraction of heat supplied that is available for external work in a diatomic ideal gas near room temperature, we need to take into consideration the specific heat capacity at constant pressure and the specific heat capacity at constant volume.

Key Points:
- Diatomic ideal gases consist of molecules with two atoms.
- The specific heat capacity at constant pressure (Cp) is the amount of heat required to raise the temperature of a substance by 1 degree Celsius at constant pressure.
- The specific heat capacity at constant volume (Cv) is the amount of heat required to raise the temperature of a substance by 1 degree Celsius at constant volume.

Calculation:
The fraction of heat supplied that is available for external work can be calculated using the following equation:

Fraction of heat available for external work = (Cp - Cv) / Cp

Explanation:
1. The specific heat capacity at constant pressure (Cp) for a diatomic ideal gas is given by the equation:

Cp = (5/2)R

where R is the gas constant.

2. The specific heat capacity at constant volume (Cv) for a diatomic ideal gas is given by the equation:

Cv = (3/2)R

3. Substituting the values of Cp and Cv into the equation for the fraction of heat available for external work:

Fraction of heat available for external work = ((5/2)R - (3/2)R) / (5/2)R

4. Simplifying the equation:

Fraction of heat available for external work = (2R/2R) / (5R/2R)

5. Canceling out the common factors:

Fraction of heat available for external work = 1 / (5/2)

6. Simplifying the equation:

Fraction of heat available for external work = 2/5

7. Converting the fraction to a decimal:

Fraction of heat available for external work = 0.4

Conclusion:
Therefore, the fraction of heat supplied that is available for external work in a diatomic ideal gas near room temperature when expanded at constant pressure is 0.4 or 40%.