Question

for an ideal monoatomic gas the internal energy U is due to the kinetic energy and U= 3/2 RT per mole, show that Cv = 3/2 per mole and Cp = 5/2 per mole​

Answer 1

Given : for an ideal monoatomic gas the internal energy U is due to the kinetic energy and U= 3/2 RT per mole.

To show : $C_v=\frac{3}{2}R$

and $C_p=\frac{5}{2}R$

solution : as it is given that, internal energy , U = 3/2 RT per mole

but we know, heat at constant volume is known as internal energy of an ideal gas.

so, $U=C_vT$ per mole

on comparing we get,

$\quad C_v=\frac{3}{2}R$

we also know, $C_p-C_v=R$

⇒$C_p=C_v+R$

⇒$C_p=\frac{3}{2}R+R=\frac{5}{2}R$

hence it is clear that molar heat at constant volume of monoatomic gas is $C_v=\frac{3}{2}R$ and at constant pressure is $C_p=\frac{5}{2}R$.

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