A gas expands with temperature according to the relation V = K T 2 / 3 , where K is a constant. Calculate work done when the temperature changes by 60 K ?

Question

A gas expands with temperature according to the relation V = K T 2 / 3 , where K is a constant. Calculate work done when the temperature changes by 60 K ?, 10 R, 30 R, 40 R, 20 R

MARKS App · Accepted Answer

dW ⁡ = PdV = RT ⁡ V ⁡ dV ⁡ … i As V = K T 2 / 3 ∴ d V = K ⁡ 2 3 T ⁡ - 1 / 3 d ⁡ T ⁡ ∴ d V V ⁡ = K ⁡ 2 3 T ⁡ - 1 / 3 d ⁡ T ⁡ KT 2 / 3 = 2 3 d ⁡ T ⁡ T ⁡ … ii From (i), W ⁡ ∫ V ⁡ 1 V ⁡ 2 RT ⁡ d V V ⁡ = ∫ T ⁡ 1 T ⁡ 2 RT 2 3 d ⁡ T ⁡ T ⁡ Using (ii) W ⁡ = 2 3 R ⁡ T ⁡ T ⁡ 1 T ⁡ 2 W ⁡ = 2 3 R ⁡ T ⁡ 2 - T ⁡ 1 = 2 3 R ⁡ × 6 0 = 4 0 R ⁡

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