Engine Operational
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Q48

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An ideal monoatomic gas is contained inside a cylinder-piston assembly connected to a Hookean spring
as shown in the figure. The piston is frictionless and massless. The spring constant is 10 kN/m. At the initial equilibrium state (shown in the figure), the spring is unstretched. The gas is expanded reversibly by adding 362.5 J of heat. At the final equilibrium state, the piston presses against the stoppers. Neglecting the heat loss to the surroundings, the final equilibrium temperature of the gas is ________ K. (rounded off to the nearest integer).
: Piston stopperPᵃᵐᵇⁱᵉⁿᵗ:1 bar
2/textMonoatomicmc/textidealgas0/textVinitial:2L01:/frac/frac/textaUnstretchedspring5cmk10KNm=2 /text{Monoatomicmc} /text{ideal} gas 0 /text{Vinitial} : 2L_{01} : /frac{/frac{/text{aUnstretchedspring}}{5cmk} 10 KN}{m} =
Tᵢₙᵢₜᵢₐₗ:300 KerA
Given For a monoatomic ideal gas, Cᵥ=3/2 R,where R=8.314 J/(molK)
GATE2025GATE 2025
Chemical Engineering
(2 Marks)

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