Internal energy of n1 moles of hydrogen at temperature T is equal to the internal energy of n2 moles of helium at temperature 2T. Then the ratio n1/n2 is

Q: Internal energy of n1 moles of hydrogen at temperature T is equal to the internal energy of n2 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)

U1 = U2

f1n1T1 = f2n2T2

n1/n2 = f2T2/f1T1 = 3×2/5×1 = 6/5

Here f2 = degrees of freedom of He = 3 and f1 = degrees of freedom of H2 = 5

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