COURSE : Detailed Explanation on Entropy Questions Lesson : Questions -(19-21
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Question 19 An adiabatic vessel contains 2 kg of water at 25 C. By paddle-wheel work transfer, the temperature of water is increased to 30 C. If the specific heat of water is assumed constant at 4.187 kJ/kg K, find the entropy change of the universe.
Solution 19 (AS)u0 303d'lT (AS)sys- |me 298 2 kg 298 K 303 298 303 K (ASuniv (AS)r 0.139340 0.13934 kJ/K
Question 20 A copper rod is of length 1 m and diameter 0.01 m. One end of the rod is at 100 C, and the other at 0 C. The rod is perfectly insulated along its length and the thermal conductivity of copper is 380 W/mK. Calculate the rate of heat transfer along the rod and the rate of entropy production due to irreversibility of this heat transfer.
Solution 20 0.01 m A = 7.854 10-5 m2 373 K K 380 W/m- K 273 K AT A X = 380 7.854 10-5 100 w = 2.9845W At the 373 K end from surrounding Q amount heat is go to the system. So at this end (AS)change373 And at the 273 K and from system Qamount of heat is rejected to the surroundings (ASare 27:3 (AS)univ.= 273-373 univ0.00293 WIK
Question 21 A body of constant heat capacity Cp and at a temperature Ti is put in contact with a reservoir at a higher temperature T. The pressure remains constant while the body comes to equilibrium with the reservoir. Show that the entropy change of the universe is equal to T, -T, T -T, - ln 1+ Prove that entropy change is positive. Given in (1 + x) = x--+ where x<1
Solution 21 Final temperature of the body will be T Let x as T> T ar (AS) body = C (AS) resoier - . Total entropy charge T-T T, (AS) in = Cr(x-ln (1 + x)} x* x x -in PL2 3 45 T-T T - T, x (3-2x) x(5-4x) 20 (AS) univ is +ve
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