Question

When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is?

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

Answer 1

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

Fraction of heat energy supplied which increase the internal energy

n = number of moles of gas

$C_v$ = specific heat at constant volume

$C_p$ = specific heat at constant pressure

$dT$ = change in temperature

$\gamma$ = ratio of specific heat of gas

$\frac{\Delta U}{\delta Q}=\frac{n{C}_{v}dT}{n{C}_{p}dT}$

$=C_v/C_p$

$=1/\gamma$

for diatomic gas,$\gamma =7/5$

hence,

$\frac{\Delta U}{\Delta Q}=1/\gamma =5/7$