Question

using the equipartition of energy concept estimate the ideal gas Cp(not Cv) in units KB for the low temperature regime where no vibrational modes are activated(if you calculate Cp=42KB, enter 42 as your answer )

Answer 1

As per equipartition theorem,

The energy of a thermodynamic system in equilibrium is partitioned equally among its degrees of freedom and molar heat capcity is given as

$C_v=\frac{d}{2}R,$

and we know that $C_p=C_v+R$

$C_p=\frac{d}{2}R+R$

where d is the degree of freedom, for ideal gas d=3

Now,

$C_v=\frac{3}{2}R, C_p=\frac{3}{2}R+R=\frac{5}{2}R$ , we know that

R=NK_B,

$R=6.022\times 10 ^{23}K_B$

$C_P=15\times10^{23}K_B$

so u need to write 15