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Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases

For an ideal gas, the ratio of molar heat capacities is C_p / C_V = 7/6 . Calculate the change in internal energy of 1.0 mole of the gas when its temperature is increased by 50 K while keeping the volume constant.

Options

  1. A0 J
  2. B2905 J
  3. C415 J
  4. D2490 J

Correct answer

D. 2490 J

Step-by-step solution

Given C_p C_V = 7 6 Using Mayer's relation, C_p - C_V = R 7 6 C_V - C_V = R C_V 6 = R C_V = 6R The change in internal energy is given by U = n C_V T Substituting n = 1 mol and T = 50 K : U = 1 6R 50 = 300R Taking R = 8.3 J K ⁻¹ mol ⁻¹ : U = 300 8.3 = 2490 J

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