Isothermal reversible expansion condition at T = 57 °C = 330 K,
Work done, W = -nRT ln(V2 / V1)
Entropy change, dS = dQ / T
We know that, dU = dQ - dW
=> dQ = dW = -nRT ln(V2 / V1) ( since dU = 0 for isothermal condition )
Clubbing above equation with the entropy change equation,
dS = dQ / T = nRT ln(V2 / V1) / T
Putting the appropriate values from the question,
dS = nRT ln(V2 / V1) / T
=> 36 = n*8.314*330 * ln(4.5 / 1.5) / 330
=> n = 3.941 moles ~ 4 moles
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