Question

At ordinary temperature, the molecule of an ideal gas has only translational and rotational kinetic energies. At high temperatures, they may also have vibrational energy. As a result of this at higher temperatures ( = molar heat capacity at constant volume)

• A. $C_v=\frac{3}{2}$ R for a monoatomic gas
• B. $C_v>\frac{3}{2}$ R for a monoatomic gas
• C. $C_v<\frac{5}{2}$ R for a diatomic gas
• D. $C_v=\frac{5}{2}$ R for a diatomic gas

Answer 1

The correct option is B $C_v>\frac{3}{2}$ R for a monoatomic gas

Vibrational Kinetic energy of a monoatomic gas = 0 at all temperatures. So,

$Cv=\frac{3}{2}R,SoCv=\frac{3}{2}R$

for a monoatomic gas even at high temperature also. In case of a diatomic gas

$Cv=\frac{3}{2}R$ at low temperatures while $Cv>\frac{3}{2}R$ at high

temperatures due to vibrational Kinetic energy.