500 gram of a diatomic gas is enclosed at a pressure of 10^5 Nm ⁻² . The density of the gas is 5 kgm ⁻³ . The energy of one mole of the gas due to its thermal motion is [consider the gas molecule as a rigid rotator]

Step-by-step solution

Energy of a diatomic gas due to thermal motion The volume is obtained from the mass and density: V = m / = 0.5 kg / 5 kg m ⁻³ = 0.1 m ^3 . From the ideal gas law, PV = nRT = 10^5 N m ⁻² 0.1 m ^3 = 10^4 J . A rigid diatomic molecule has five degrees of freedom: three translational and two rotational, so f = 5 . The internal energy becomes U = 5 2 nRT = 5 2 10^4 J = 2.5 10^4 J . Since the problem refers to "the gas" and the mass is given, this result corresponds to the total internal energy of the sample, matching op