Question

5 kg of water substance at 1 bar, 400 K, contained in a piston-cylinder apparatus, is compressed to 10 bar, with heat transfer to a reservoir maintained at 350 K; the temperature of the water substance remains constant at 400 K. If the initial and final specific entropies of the water substance are: 7.502 kJ/kg-K and 1.600 kJ/kg-K respectively;

(a)How much heat is removed?

(b)What is the entropy change of the water substance?

(c)What is the entropy change of the reservoir?

(d)Show that the process is possible

Answer 1

Theory: we need to apply the formual that Entropy change = Heat given/Temperature

Solution:

Stage 1: 1 bar 400 K, stage 2: 10 bar 400 K, Temperature of resorvior = 350K

mass of water = 5 Kg.

A) Heat given to system = Total entropy changed of water* Temeprature of water

= (Final specific entropy-initial specific entropy)*mass of water*Temperature of water

= (1.6-7.502)*5*400 = -11804 kJ

so heat released = (-) heat given = 11804 kJ

B) Entropy change of water substance = (Final specific entropy-initial specific entropy)*mass of water

=(1.6-7.502)*5 = -29.51 kJ/K

C) Entropy change of resorvior = heat given to resorvior/Temperature of resorvior

= 11804/350 = 33.73 kJ/K

D) Entropy change of universe = entropy change of system +entropy change of resorvior

= -29.51+33.73 = 4.22 kJ/K

Since the entropy change of universe is positive that means the process is possible. If entropy change of univers was negative then process would have not been possible.

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