Assignment=5
Entropy
Q1 The latent heat of fusion of water at 0°C is 335 kJ/kg. How much does the entropy of 1 kg of
ice change as it melts into water at 0°C.
(Ans. 1.2271 kJ/K)
Q2 Two kg of water at 80°C are mixed adiabatically with 3 kg of water at 30°C in a constant
pressure process of 1 atmosphere. Find the increase in the entropy of the total mass of water due
to the mixing process (cp of water = 4.187 kJ/kg K).
(Ans. 0.0576 kJ/K)
Q3 A heat engine receives reversibly 420 kJ/cycle of heat from a source at 327°C, and rejects
heat reversibly to a sink at 27°C. There are no other heat transfers. For each of the three
hypothetical amounts of heat rejected, in (a), (b), and (c) below, compute the cyclic integral of
dQ /T. from these results show which case is irreversible, which reversible, and which
impossible:
(a) 210 kJ/cycle rejected
(b) 105 kJ/cycle rejected
(c) 315 kJ/cycle rejected
(Ans. (a) Reversible, (b) Impossible, (c) Irreversible)
Q4 Water is heated at a constant pressure of 0.7 MPa. The boiling point is 164.97°C. The initial
temperature of water is 0°C. The latent heat of evaporation is 2066.3 kJ/kg. Find the increase of
entropy of water, if the final state is steam.
(Ans. 6.6967 kJ/kg K)
Q5 Ten grammes of water at 20°C is converted into ice at –10°C at constant atmospheric
pressure. Assuming the specific heat of liquid water to remain constant at 4.2 J/gK and that of ice
to be half of this value, and taking the latent heat of fusion of ice at 0°C to be 335 J/g, calculate
the total entropy change of the system.
(Ans. 16.02 J/K)
Q6 Calculate the entropy change of the universe as a result of the following processes:
(a) A copper block of 600 g mass and with Cp of 150 J/K at 100°C is placed in a lake at 8°C.
(b) Two such blocks, at 100 and 0°C, are joined together.
(Ans. (a) 6.69 J/K, (b) 3.64 J/K)
Q7 A system maintained at constant volume is initially at temperature T1, and a heat reservoir at
the lower temperature T0 is available. Show that the maximum work recoverable as the system is
cooled to T0 is
𝑇1
W=Cv[(T1-To)-To ln𝑇𝑜
Q8 If the temperature of the atmosphere is 5°C on a winter day and if 1 kg of water at 90°C is
available, how much work can be obtained. Take cv, of water as 4.186 kJ/kg K.
Q9 A reversible engine, as shown in Figure during a cycle of operations draws 5 MJ from the
400 K reservoir and does 840 kJ of work. Find the amount and direction of heat interaction with
other reservoirs.
(Ans. Q2 = + 4.98 MJ and Q3 = – 0.82 MJ)
Assignment=5
Entropy
Q10 Two blocks of metal, each having a mass of 10 kg and a specific heat of 0.4 kJ/kg K, are at
a temperature of 40°C. A reversible refrigerator receives heat from one block and rejects heat to
the other. Calculate the work required to cause a temperature difference of 100°C between the
two blocks.
(Ans. Wmin = 31.87 kJ)
Q11 A lump of ice with a mass of 1.5 kg at an initial temperature of 260 K melts at the pressure
of 1 bar as a result of heat transfer from the environment. After some time has elapsed the
resulting water attains the temperature of the environment, 293 K. Calculate the entropy
production associated with this process. The latent heat of fusion of ice is 333.4 kJ/kg, the
specific heat of ice and water are 2.07 and 4.2 kJ/kg K
respectively, and ice melts at 273.15 K.
(Ans. 0.1514 kJ/K)