Question

The translational kinetic energy of molecules of one mole of a monoatomic gas is U = 3NkT/2. The value of atomic specific heat of gas under constant pressure will be:

• A. $\frac{3}{2}R$
• B. $\frac{5}{2}R$
• C. $\frac{7}{2}R$
• D. $\frac{9}{2}R$

Answer 1

The correct option is B $\frac{5}{2}R$

given that

energy(U)= $\frac{3}{2}NkT$ (Where N=avagadro number, k=boltzman constant)

as we know that universal gas constant (R)= kN

So. above expression becomes,

$U=\frac{3}{2}RT$

Now,

Specific heat of gas under constant volume, $C_V=\frac{\partial U}{\partial T}$

$\Rightarrow C_V=\frac{\partial \left(\frac{3}{2}RT\right)}{\partial T}$

$\Rightarrow C_V=\frac{3}{2}R$

Now, Specific heat of gas under constant pressure, $C_P=C_V+R$

$\Rightarrow C_P=\frac{3}{2}R+R=\frac{5}{2}R$