Q: Internal energy of n_{1} moles of hydrogen at temperature T is equal to the internal energy of n_{2} moles of helium at temperature 2T. Then the ratio n1/n2 is

(a)3/5

(b)2/3

(c)6/5

(d)3/7

Solution :(c)

Internal energy of n moles of an ideal gas at temperature T is given by:

$ \displaystyle U = \frac{1}{2}f n R T $

Where , (f = degrees of freedom)

U_{1} = U_{2}

f_{1}n_{1}T_{1} = f_{2}n_{2}T_{2}

n_{1}/n_{2} = f_{2}T_{2}/f_{1}T_{1} = 3×2/5×1 = 6/5

Here f_{2} = degrees of freedom of He = 3 and f_{1} = degrees of freedom of H_{2} = 5