A mass m = 275 kg of lava at T_H = 915 degree C emerges from a volcano deep in t

Question

A mass m = 275 kg of lava at T_H = 915 degree C emerges from a volcano deep in the ocean. At this depth, the ocean water is at a temperature of T_c = 1.8 degree C, and the lava cools and solidifies. The specific heat capacity of the lava for this process is c = 840 J/kg middot degree C and the latent heat of fusion of the lava is L_f = 4.0 times 10^5 J/kg. Assume that the temperature of the ocean does not change in this process. The lava cools to 700.0 degree C before solidifying. What is the change in entropy delta S_1 of the lava in joules per kelvin during this process? Calculate the change in entropy of the ocean waters delta S_2 in joules per kelvin during the cooling of the molten lava. Calculate the change in entropy of the lava delta S_3 in joules per kelvin when it solidifies. Calculate the entropy change of the ocean delta S_4 in joules per kelvin due to the solidification of the lava. Does this process obey the second law of thermodynamics?

Explanation / Answer

Q = m c deltaT

and S = integral of Q/t = m c dT/T = m c ln(Tf/Ti)

(A) S1 = 275 x 840 x ln((700 + 273) / (273 + 915))

S1 = -46117.4 J/K

(B) temp of ocean is constant hence

S2 = Q / T

T = 273 + 1.8 = 274.8 K

Q = m c deltaT = 275 x 840 x (915-700) = 4.9665 x 10^7 J

S2 = 180731.4 J/K

(C) solidify happens at constant temp.

so S3 = Q/T

Q = m Lf = 275 x 4 x 10^5 = - 1.1 x 10^8 J

T = 273 + 700 = 973 K

S3 = - 113052.42 J/K

(D) Q = + 1.1 x 10^8 J

T = 273 + 1.8 = 274.8 K

S4 = 400291.12 J/K

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