Question

A diatomic gas is heated at constant pressure. The fraction of heat energy used to increase the internal energy is

• A. $\frac{3}{5}$
• B. $\frac{3}{7}$
• C. $\frac{5}{7}$
• D. $\frac{5}{9}$

Answer 1

The correct option is C $\frac{5}{7}$

Heat energy added$=$change in internal energy$+$work done
$\Delta Q=\Delta U+\Delta W$
At constant pressure,
$n{C}_p\Delta T=n{C}_v\Delta T+nR\Delta T$
Fraction of heat energy used to increase internal energy$=\frac{n{C}_v\Delta T}{n{C}_v\Delta T+nR\Delta T}$
$=\frac{C_v}{C_v+R}=\frac{C_v}{C_p}=\frac{1}{\gamma }=\frac{1}{\frac{7}{5}}=\frac{5}{7}$
Option C.