EG-210 Tutorial Sheet No. 2 (2014)

The Second Law of Thermodynamics and Cyclic Processes

Please complete and hand-in Question 5 by 3pm Monday 10th

March 2014.

1) (a) Steam enters a horizontal pipe operating at steady state with a specific enthalpy of 3000

kJ/kg and a mass flow rate of 0.5 kg/s. At the exit, the specific enthalpy is 1700 kJ/kg. If

there is no significant change in kinetic energy from inlet to exit, determine the rate of heat

transfer between the pipe and its surroundings, in kW.

[5 marks]

(b) Steam enters a well-insulated turbine operating at steady state at 4 MPa with a specific

enthalpy of 3015.4 kJ/kg and a velocity of 10 m/s. The steam expands to the turbine exit

where the pressure is 0.07 MPa, specific enthalpy is 2431.7 kJ/kg, and the velocity is 90 m/s.

The mass flow rate is 11.95 kg/s. Neglecting potential energy effects, determine the power

developed by the turbine, in kW.

[5 marks]

(c) Steam enters a turbine operating at steady state with a mass flow of 10 kg/min, a specific

enthalpy of 3100 kJ/kg, and a velocity of 30 m/s. At the exit, the specific enthalpy is 2300

kJ/kg and the velocity is 45 m/s. The elevation of the inlet is 3 m higher than at the exit. Heat

transfer from the turbine to its surroundings occurs at a rate of 1.1 kJ per kg of steam flowing.

Let g = 9.81 m/s2. Determine the power developed by the turbine, in kW.

[5 marks]

(d) Air enters a compressor operating at steady state at 1 atm with a specific enthalpy of 290

kJ/kg and exits at a higher pressure with a specific enthalpy of 1023 kJ/kg. The mass flow

rate is 0.1 kg/s. If the compressor power input is 77 kW, determine the rate of heat transfer

between the compressor and its surroundings, in kW. Neglect kinetic and potential energy

effects and assume the ideal gas model.

[5 marks]

(e) A pump delivers water through a hose terminated by a nozzle. The exit of the nozzle has a

diameter of 2.5 cm and is located 4 m above the pump inlet pipe, which has a diameter of 5.0

cm. The pressure is equal to 1 bar at both the inlet and the exit, and the temperature is

constant at 20 C. The magnitude of the power input required by the pump is 8.6 kW and the

acceleration due to gravity, g = 9.81 m/s2. The specific volume of water at 20 C and 1 bar is

1.0018 10-3

m3/kg. Determine the mass flow rate delivered by the pump in kg/s.

[5 marks]

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2) (i) The data listed below are claimed for a power cycle operating between hot and cold

reservoirs at 1000 K and 300 K, respectively. For each case, determine whether the cycle

operates reversibly, operates irreversibly, or is impossible.

(a) Qh = 600 kJ, Weng = 300 kJ, Qc = 300 kJ

(b) Qh = 400 kJ, Weng = 280 kJ, Qc = 120 kJ

(c) Qh = 700 kJ, Weng = 300 kJ, Qc = 500 kJ

(d) Qh = 800 kJ, Weng = 600 kJ, Qc = 200 kJ

[4 marks]

(ii) A reversible power cycle operating between hot and cold reservoirs at 1000 K and 300 K,

respectively, receives 100 kJ by heat transfer from the hot reservoir for each cycle of

operation. Determine the net work developed in 10 cycles of operation, in kJ.

[3 marks]

(iii) In a heat-treating process, a 1 kg metal part, initially at 1075 K, is quenched in a tank

containing 100 kg of water, initially at 295 K. There is negligible heat transfer between the

contents of the tank and their surroundings. The metal part and water can be modeled as

incompressible with specific heats 0.5 kJ/kg K and 4.2 kJ/kg K, respectively. Determine (a)

the final equilibrium temperature after quenching, in K, and (b) the amount of entropy

produced within the tank, in kJ/K.

[6 marks]

(iv) Propane at 0.1 MPa, 20 C enters an insulated compressor operating at steady state and

exits at 0.4 MPa, 90 C Neglecting kinetic and potential energy effects, determine (a) the power required by the compressor, in kJ per kg of propane flowing. (b) the rate of entropy

production within the compressor, in kJ/K per kg of propane flowing. Data supplied: at 0.1

MPa, 20 C hpropane = 517.6 kJ/kg and spropane = 2.194 kJ/kg K, at 0.4 MPa, 90 C hpropane = 639.2 kJ/kg and spropane = 2.311 kJ/kg K,

[6 marks]

(v) The pressurevolume diagram of a Carnot power cycle executed by an ideal gas with

constant specific heat ratio is shown below. Show that V4V2 = V1V3.

[6 marks]

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3) A heat engine cylinder contains 0.1 kg of air. The engine is assumed to operate on a Carnot

cycle comprising the following four processes:

Step A-B: Isothermal expansion at 1000 K during which the volume of the air is

doubled.

Step B-C: Adiabatic expansion until the temperature of the air reaches 350 K and the

pressure 1 bar.

Step C-D: Isothermal compression of the air at 350 K.

Step D-A: Adiabatic compression until the air temperature reaches 1000 K and the

cycle is complete.

Assuming that air behaves as an ideal gas and given the following data (specific heat capacity

of air in a constant volume process CV = 0.7175 kJ kg-1

K-1

; Gas constant for air R = 0.2867

kJ kg-1

K-1

), then

a) Sketch the cycle on a P-V diagram.

b) What is the maximum pressure achieved in the cycle?

c) Show that the volume of air is halved during the isothermal compression.

d) Calculate the work done during each of the adiabatic processes.

e) Calculate the heat and thus work effects for each of the isothermal processes.

f) Determine the net work done per cycle.

g) Confirm the cycle efficiency matches the prediction given by = 1 (Tc/Th)

[25 marks]

4

4) At the Bear Point refinery complex on the St Lawrence Seaway between Canada and the

USA, the process waste gas is being considered as a thermal energy source for raising steam

to generate electrical power in an energy park associated with the refinery. The preliminary

design of a Rankine Cycle steam turbine power plant is being considered to make use of this

thermal energy. In the proposed design, steam is to be supplied from a boiler to the turbine

inlet at a pressure of 15 MPa and temperature of 600 C whilst the exhaust pressure from the

turbine is 10 kPa. The exhaust mixture is passed through a condenser and then pumped back

to the boiler. The power plant is assumed to be a closed system.

a) Draw a block flow diagram of the proposed power plant and a general Temperature-

Entropy diagram of the cycle, labelling the appropriate points.

[6 marks]

b) Calculate the operational data for the steam/water after each step of the cycle, namely:

temperature, pressure, quality, specific enthalpy, specific entropy. State any assumptions you

make.

[12 marks]

c) Calculate the thermal efficiency of the cycle.

[2 marks]

d) Determine the flow rate of water/steam required to produce 60 MW.

[2 marks]

e) What methods could be employed to improve the thermal efficiency of the cycle?

[3 marks]

Data supplied:

Data Sheet No. (1): Steam Tables.

The specific volume of water at 10 kPa is: = 0.00101 kg m-3

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5) Refrigerant 134a is the working fluid in an ideal vapour-compression refrigeration cycle

that communicates thermally with a cold region at -4C (minus four) and a warm region at

24C. Saturated vapour enters the compressor at -4C and saturated liquid leaves the

condenser at 24C. The mass flow rate of the refrigerant is 0.2 kg/s.

a) Draw a block flow diagram of the proposed refrigeration plant and explain how the

refrigeration cycle works.

[5 marks]

b) Draw a Temperature-Entropy diagram of the cycle, labelling the appropriate points.

[2 marks]

c) Calculate the operational data for the refrigerant after each step of the cycle, namely:

temperature, pressure, quality, specific enthalpy and specific entropy. State any assumptions

you make.

[10 marks]

d) Calculate the compressor power, in kW.

[2 marks]

e) Calculate the refrigeration capacity, in kW.

[2 marks]

f) Determine the coefficient of performance of the ideal vapour-compression refrigeration

cycle.

[2 marks]

g) Determine the coefficient of performance of an ideal Carnot refrigeration cycle operating

at the same conditions.

[2 marks]

Data Supplied:

Data Sheet No. (2): Properties of Refrigerant 134a.

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DATA SHEET No. (1): Steam Tables

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DATA SHEET No. (1):Continued Steam Tables

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DATA SHEET No. (1):Continued Steam Tables

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DATA SHEET No. (2): Properties of Refrigerant 134a

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DATA SHEET No. (2): Properties of Refrigerant 134a (Continued)

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DATA SHEET No. (2): Properties of Refrigerant 134a (Continued)