4 moles of an ideal gas are heated in a rigid container such that its internal energy increases by 4160 J . If the molar heat capacity of the gas at constant pressure is 29.1 J K ⁻¹ mol ⁻¹ , the change in temperature of the gas is ________

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4 moles of an ideal gas are heated in a rigid container such that its internal energy increases by 4160 J . If the molar heat capacity of the gas at constant pressure is 29.1 J K ⁻¹ mol ⁻¹ , the change in temperature of the gas is ________ K . (Given: R = 8.3 J K ⁻¹ mol ⁻¹ )

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Correct answer: 50

For an ideal gas, the molar heat capacity at constant volume is given by Mayer's relation: C_ v,m = C_ p,m - R C_ v,m = 29.1 - 8.3 = 20.8 J K ⁻¹ mol ⁻¹ The change in internal energy of the gas is given by: U = n C_ v,m T 4160 = 4 20.8 T 4160 = 83.2 T T = 4160 83.2 = 50 K Answer: 50

4 moles of an ideal gas are heated in a rigid container such that its internal energy increases by 4160 J . If the molar heat capacity of the gas at constant pressure is 29.1 J K ⁻¹ mol ⁻¹ , the change in temperature of the gas is ________ K . (Given: R = 8.3 J K ⁻¹ mol ⁻¹ )

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