The internal energy of n 1 mol of hydrogen of temperature T is equal to the internal energy of n 2 mol of helium at temperature 2 T . What will be the value of the ratio n 1 n 2 ?

Step-by-step solution

The internal energy of n moles of an ideal gas at temperature T is given by U = f ⁡ 2 nRT ( 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 = 1 . 2 Here, f ⁡ 2 = degrees of freedom of He = 3 and, f ⁡ 1 = degrees of freedom of H 2 = 5