An ideal gas has a molar heat capacity ratio of C_p / C_V = 7/6 . Determine the change in internal energy of 1.0 mole of this gas when its temperature is raised by 50 K while keeping the pressure constant.

Step-by-step solution

Given C_p C_V = 7 6 For an ideal gas, C_p - C_V = R 7 6 C_V - C_V = R 1 6 C_V = R C_V = 6R The change in internal energy of an ideal gas depends only on the change in temperature and is given by U = n C_V T Substituting n = 1 mol , C_V = 6R , and T = 50 K : U = 1 6R 50 = 300R Using R = 8.3 J mol ⁻¹ K ⁻¹ : U = 300 8.3 = 2490 J