The ratio of molar heat capacities for an ideal gas is given as C_p / C_V = 7/6 . Find the change in internal energy of 1.0 mole of the gas when its temperature is raised by 50 K adiabatically.

Step-by-step solution

Given the ratio of molar heat capacities = C_p C_V = 7 6 The molar heat capacity at constant volume C_V is given by: C_V = R - 1 = R 7 6 - 1 = 6R The change in internal energy for an ideal gas depends only on the change in temperature and is given by: U = n C_V T Substituting the given values n = 1.0 mol and T = 50 K : U = 1.0 6R 50 = 300R Using the universal gas constant R = 8.3 J mol ⁻¹ K ⁻¹ : U = 300 8.3 = 2490 J