Question

When an ideal diatomic gas is heated at constant pressure then the fraction of heat energy which is used to increase the internal energy of gas system, is

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

Answer 1

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

Heat at constant pressure,

$\Delta Q=n{C}_P\Delta T$. . . . . . .(1)

where, $n=$ no. of moles

$C_P=$ molar heat capacity at constant pressure

for diatomic gas, $C_P=\frac{7R}{2}$, $C_V=\frac{5R}{2}$

So, $\Delta Q=n\left(\frac{7R}{2}\right)\Delta T$. . . . . .(2)

Change in internal energy at constant volume,

$\Delta U=n{C}_V\Delta T$

$\Delta U=n\left(\frac{5R}{2}\right)\Delta T$. . . . .(3)

ratio, $\frac{\Delta U}{\Delta Q}=\frac{n\frac{5R}{2}\Delta T}{n\frac{7R}{2}\Delta T}=\frac{5}{7}$

Hence, $5/7$ part of heat supplied is used to increase the internal energy

The correct option is C.