Question

An ideal mono-atomic gas of given mass is heated at constant pressure. In this process, the fraction of supplied energy used for the increase of the internal energy of the gas is

• A. $\frac{3}{8}$
• B. $\frac{3}{5}$
• C. $\frac{3}{4}$
• D. $\frac{2}{5}$

Answer 1

Answer: (B)

$\frac{3}{5}$

Let the change in temperature of the gas be $\Delta T$.

Thus, the amount of heat supplied under constant pressure is $Q=C_P\Delta T$

The change in internal energy is $\Delta U=C_V\Delta T$

Thus, the fraction of energy used for internal energy is $\frac{\Delta U}{Q}=\frac{C_V}{C_P}$

For a mono-atomic ideal gas, $C_V=3R/2$ and $C_P=5R/2$

Thus, $\frac{\Delta U}{Q}=\frac{C_V}{C_P}=\frac{3R/2}{5R/2}=\frac{3}{5}$