Question

An ideal diatomic gas is heated at constant pressure. What fraction of heat energy is utilized to increase its internal energy?

• A. $\frac{5}{7}$
• B. $\frac{2}{5}$
• C. $\frac{3}{5}$
• D. $\frac{3}{7}$

Answer 1

Answer: (A)

$\frac{5}{7}$

Total heat energy supplied to raise temperature of a diatomic gas at constant pressure=$n{C}_p\Delta T$

Total rise in internal energy=$n{C}_v\Delta T$

Thus fraction of heat energy utilized in increasing internal energy=$\frac{n{C}_v\Delta T}{n{C}_p\Delta T}$

$=\frac{C_v}{C_p}=\frac{\frac{f}{2}}{\frac{f}{2}+1}$

$=\frac{f}{f+2}$

where $f$ is the number of degrees of freedom of the gas.

For diatomic gas, $f=5$

Thus fraction=$\frac{5}{7}$