A process for monoatomic gas is defined by V = aT 2 , where a is a constant. In this process temperature of 1 mole of a gas is increased by 100 K; then (V = Volume, T = Temperature )

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V = aT 2 ⇒ PV 1/2 = const C = 1 − x R ​ + γ − 1 R ​ 1 − 2 1 ​ R ​ + 3 5 ​ − 1 R ​ = 2 7 R ​ V = aT 2 dV = 2 aTdT P = V nRT ​ = aT 2 nRT ​ = aT nR ​ PdV = ( aT nR ​ ) 2 aTdT = 2 nRdT From eqn. (1) W = ∫ PdV = ∫ T 1 ​ T 2 ​ ​ 2 nR dT = 2 nR Δ T W = ( 2 ) ( 1 ) ( R ) ( 100 ) = 200 R

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