Answer to Question #122318 in Mechanical Engineering for INDRAJIT SOMNATH WADGAVE

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