Evaluation of Entropy Change

From equation:

1.   
2.   

Example 1.18: A heat engine having an efficiency of 35% is used to run a refrigerator of COP of 4, what is the heat input into the each MJ removed from the cold body by the refrigerator? If this system is used as a heat pump (Figure 1.16), how many MJ of heat would be available for heating for each MJ of heat input to the engine?

Figure 1.16 Heat Reservoir and Sink

Solution:

Example 1.19: A heat pump working on a Carnot cycle takes in heat from a reservoir at 8°C and delivers heat to the reservoir at 50°C. The heat pump is driven by a reversible heat engine taking heat from a reservoir at 850°C and rejecting heat to reservoir at 50°C (Figure 1.17). The reversible heat engine also drives a machine of input required of 25 kW. If the heat pump extracts 15 kJ/sec from the 8°C reservoir, determine (a) the rate of heat supply from the 850°C source, and (b) the rate of heat rejection to 50°C sink.

Figure 1.17 Heat Pump and Heat Engine

Solution:

Example 1.20: A reversible heat engine as shown in Figure 1.18 during a cycle of operation draws 5 MJ from the 400 K reservoir and does 840 kJ work. Find the amount and direction of heat interaction with other reservoirs.

Figure 1.18 Reversible Heat Engine

Solution:

Solving Eqs (1.1) and (1.2), we get

Example 1.21: Two blocks of metal each of mass M and specific heat C, initially at absolute temperature T₁ and T₂, respectively, brought to the same final temperature T_f by means of reversible process. Derive an expression for the amount of work obtained during the process in terms of M, C, T₁ and T₂.

Solution:

Let T₁ > T₂ and final temperature be T_f.

For reversible process, total entropy = 0

Example 1.22: An insulated tank of 1 m³ volume contains air at 0.1 MPa and 300 K. The tank is connected to high pressure line in which air at 1 MPa and 600 K flows. The tank is quickly filled with air by opening the valve between the tank and high pressure line. If the final pressure of air in tank is 1 MPa (Figure 1.19), determine the mass of air which enters the tank and the entropy change associated with filling process. Take universal gas constant  = 8.314 kJ/kg mole K.

Figure 1.19 Insulated Tank

Solution:

Let final mass of air inside the cylinder = m₂

Final temperature of air inside the cylinder = T

From Eqs (1.3) and (1.4)

Entropy change associated with the process = ΔS₁ + ΔS₂ = 0.88261 kJ/K

Example 1.23: Ten kilograms of water at 0°C is brought into contact of a heat reservoir at 100°C, where water temperature becomes 100°C. Find the entropy change of water, reservoir and universe.

Solution:

Example 1.24: Calculate the entropy change when 5 kg of water at 20°C is mixed with 5 kg of water at 100°C. The specific heat of water is 4.18 kJ/kg.

Solution:

Let T_f is final temperature