Two moles of an ideal gas undergo reversible isothermal expansion from a volume of 10 L to 100 L at 300 K . What is the amount of heat absorbed by the gas in this process? (Given: R = 8.314 J K ⁻¹ mol ⁻¹ and 2.303 8.314 300 5744 J )

Step-by-step solution

For an isothermal process involving an ideal gas, the temperature remains constant, so the change in internal energy is zero ( U = 0 ). According to the First Law of Thermodynamics: U = q + W 0 = q + W q = -W The work done during reversible isothermal expansion is calculated as: W = -2.303 nRT ( V₂ V₁ ) Substituting the given values ( n = 2 moles , V₁ = 10 L , V₂ = 100 L ): W = -2.303 2 8.314 300 ( 100 10 ) W = -2 (2.303 8.314 300) (10) W = -2 5744 1 W = -11488 J = -11.488 kJ -11.49 kJ The negative sign indicates t