A 50kg block of iron casting at 500K is thrown into a large lake which is at a temperature of 285K.?

The iron block eventually reaches thermal equilibrium with the lake water. Assuming an average specific heat of 0.45kJ/kg-K for the iron, determine (a) the entropy change of the iron block, (b) the entropy change of the lake water, and (c) the total entropy change for the process?

A 50kg block of iron casting at 500K is thrown into a large lake which is at a temperature of 285K.?
Specific heat of iron block:


Cv = m cv = 22.5 kJ/K





Entropy of iron:


S(T) = ∫dS = ∫ 1/T CvdT = Cv lnT








Entropy change of iron:


∆Si = Cv ln(To/T) = -12.65 kJ/K





Entropy change of water:


∆Sw = ∆Q/To = Cv(T/To -1) = +16.97 kJ/K





Total entropy change:


∆S = ∆SI + ∆Sw = +4.3 kJ/K
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