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JEE MainChemistryThermodynamics (C)

An ideal gas is enclosed in a cylinder fitted with a frictionless movable piston. The gas is heated by a 120 W electric heater for 50 s at constant pressure. During this process, the gas expands and does 1000 J of work on the surroundings. If the temperature of the gas increases by 10 K, the heat capacity of the gas at constant volume is _____ J K ⁻¹ .

Correct answer

500

Step-by-step solution

The total heat supplied to the gas at constant pressure is: q_p = P t = 120 W 50 s = 6000 J According to the First Law of Thermodynamics: U = q - W Given that the work done by the gas (expansion work) is W = 1000 J, the change in internal energy is: U = 6000 - 1000 = 5000 J The change in internal energy is related to the heat capacity at constant volume ( C_v ) by: U = C_v T Given T = 10 K, we have: 5000 = C_v 10 C_v = 5000 10 = 500 J K ⁻¹ Answer: 500

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