(a) 1 kg of water at 300 K is brought into contact with a heat reservoir at 600

Question

(a) 1 kg of water at 300 K is brought into contact with a heat reservoir at 600 K. When the water has reached 600 K, what is the entropy change of the water? Of the heat reservoir? Of the universe? (The heat capacity of water is 1 cal/gm-K)

(b) If the water had been heated from 300 K to 600 K by first bringing it into contact with a reservoir at 400 K and then with a reservoir at 600 K, what would have been the entropy change of the universe?

(c) Explain how the water might be heated from 300 K to 600 K with almost no change of entropy of the universe.

Explanation / Answer

a) Entropy Change of Water Cp* ln (To / T) = 4.184 * ln (600 / 300) = 2.9 kJ / k Heat Taken up = m Cp (To - T) = 1 * 4.184 * 300 = 1255.2 kJ Heat given by Heat Reservoir = 1255.2 kJ... Hence, change in entropy of Reservoir= Q / T = - 1255.2 / 600 = - 2.092 kJ /K Hence change in entropy of universe = 2.9 - 2.092 = 0.808 kJ /K b) Entropy Change of water = Cp ln (400 / 300) + Cp ln (600 / 400) = 1.203 + 1.696 = 2.9 kJ / K Heat given up by reservoir at 400 K = 4.184 ( 400 - 300) kJ = 418.4 K Entropy Change of this reservoir = 418.4 / 400 = - 1.046 kJ / k Heat given up by reservoir at 600 K = 4.184 ( 600 - 400) kJ = 836.8 K Entropy Change of this reservoir = - 836.8 / 600 =-1.394 kJ / k So, entropy change of universe = 2.9 - 1.046 - 1.394 = 0.46 kJ / k c) Water can be heated tfrom 300 K to 600 with absolutely no change in entropy of the universe, by heating it in stages with infinite number of heat reservoirs...so that difference in temperature of water and reservoir at each stage is infinitesimally small... It is clear from parts a and b, that...with 2 reservoir, the entropy change decrease...as the number of reservoir will increase, the entropy change will keep decreasing...and at infinite no of reservoir, it will become zero...

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.