1) A 2.41 mol sample of an ideal gas expands reversibly and isothermally at 403

Question

1) A 2.41 mol sample of an ideal gas expands reversibly and isothermally at 403 K until its volume is doubled. What is the increase in entropy of the gas?

2)A 30.6 g block of copper whose temperature is 435 K is placed in an insulating box with a 125 g block of lead whose temperature is 127 K. (a) What is the equilibrium temperature of the two-block system? (b) What is the change in the internal energy of the two-block system between the initial state and the equilibrium state? (c) What is the change in the entropy of the two-block system? The heat capacities of copper and lead are 386 J/kg

Explanation / Answer

1) Entropy change = nR ln(V2/V1)

= 2.41 * 8.314 * ln (2)       as volume is doubled

= 13.89 J K-1

2) (a) Suppose the equilibrium temp is T. At equilibrium,

Heat absorbed by lead = Heat given up by copper

or 125 * 0.128 * (T - 127) = 30.6 * 0.386 * (435 - T)        specific heats in J/g K

or 16 (T - 127) = 11.81 (435 - T)

or T (16 + 11.81) = 5137.35 + 2032

or T = 257.8 K

(b) As there is no chnage in volume, net work done = 0

So change in internal energy = net heat transfer

= 125 * 0.128 * (257.8 - 127) - 30.6 * 0.386 * (435 - 257.8)

= 2092.8 - 2093

= 0.2 J

(c) Entropy change = net heat change / T = 0.2 / 257.8 = 7.76 * 10-4 J K-1

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