1. There is a well-insulated box, if we fill with 100kg water at 50 \'C and then

Question

1. There is a well-insulated box, if we fill with 100kg water at 50 'C and then put a 50 kg carbon steel ball at 75 C into the box. Hint: Cp, carbon steel- 0.12 (kcal/(kg*K)) (a) Find the common temperature of the water and Carbon Steel ball after the passage of a (b) (c) (d) long period of time. What is the entropy change of the water in going from its initial to final state? What is the entropy change of the copper ball in going from its initial to final state? What is the entropy change of the composite system of ball and water in going from its initial to final state?

Explanation / Answer

Part a

Heat gained by water = heat loss by steel

Mass of water x Cpw x (T-50) = Mass of steel x Cp x (T2-T)

100 kg x 1 kcal/kgK x (T-50) = 50 kg x 0.12 kcal/kgK x (75-T)

100 T - 5000 = 450 - 6T

T = 51.415°C = 324.42K

Part b

Entropy change of water = mass x Cpw x ln (T2/T1)

= 100 kg x 1 kcal/kgK x ln (324.42/323)

= 0.438 kcal/K

Part C

Entropy change of ball = mass x Cp x ln (T2/T1)

= 50 kg x 0.12 kcal/kgK x ln (324.42/348)

= - 0.421 kcal/K

Part d

Entropy change of system = 0.438 - 0.421 = 0.017 kcal/K

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