One mole of an ideak gas consisting of monatomic molecules is enclosed in a vessel at a temperature `T_0 = 300 K`. How many times and in what way will the statistical weight of this system (gas) vary if it heated isochorically by `Delta T = 1.0 K` ?

Explanation

For a monoatomic gas `C_V = (3)/(2) R` per mole
The entropy change in the process is
`Delta S = S - S_0 = int_(T_0)^(T_0 + Delta T) C_V (dT)/(T) = (3)/(2) R 1n (1 + (Delta T)/(T_0))`
N ow from the Boltzmann equation
`S = k 1n Omega`
`(Omega)/(Omega_0) = e^((S - S_0)//k) = (1 + (Delta T)/(T_0))^((3 N_A)/(2)) = (1 + (1)/(300))^((3 xx 6)/(2) xx 10^23) = 10^23 xx 10^21`
Thus the statistical weight increases by this factor.