MAAE3400 Problem Set 01

MAAE 3400: APPLIED THERMODYNAMICS PROBLEM SET 1

Chapter 2: Energy and the First Law of Thermodynamics

1 Problem 2.55, Page 75

A mass of 10 kg undergoes a process during which there is heat transfer from the mass at a

rate of 5 kJ per kg, an elevation decrease of 50 m, and an increase in velocity from 15 m/s to

30 m/s. The specific internal energy decreases by 5 kJ/kg and the acceleration of gravity is

constant at 9.7 m/s2. Determine the work for the process, in kJ. (Answer: 1.47 kJ)

Chapter 3: Evaluating Properties


Water is contained in a closed, rigid, 0.2 m3 tank at an initial pressure of 5 bar and a quality of

50%. Heat transfer occurs until the tank contains only saturated vapor. Determine the final

mass of vapor in the tank, in kg, and the final pressure, in bar. (Answers: 1.064 kg, 10.5 bar)


One kilogram of water initially is at the critical point. (a) If the water is cooled at constant-

specific volume to a pressure of 30 bar, determine the quality at the final state. (b) If the

water undergoes a constant-temperature expansion to a pressure of 30 bar, determine the

specific volume at the final state, in m3/kg. (Answers: a) 0.0296, b) 0.0948 m3/kg)


A piston-cylinder assembly contains 1 kg of water, initially occupying a volume of 0.5 m3 at 1

bar. Energy transfer by heat to the water results in an expansion at constant temperature to a

final volume of 1.694 m3. Kinetic and potential energy effects are negligible. For the water, (a)

show the process on a Tv diagram, (b) evaluate the work, in kJ, and (c) evaluate the heat

transfer, in kJ. (Answers: b) 119.4 kJ, c) 1592 kJ)

Chapter 4: Control Volume Analysis Using Energy


Refrigerant 134a enters a horizontal pipe operating at steady state at 40C, 300 kPa and a

velocity of 40 m/s. At the exit, the temperature is 50C and the pressure is 240 kPa. The pipe

diameter is 0.04 m. Determine (a) the mass flow rate of the refrigerant, in kg/s, (b) the

velocity at the exit, in m/s, and (c) the rate of heat transfer between the pipe and its

surroundings, in kW. (Answers: a) 0.621 kg/s, b) 52.23 m/s, c) 6.82 kW)



Steam enters the first-stage turbine shown in the figure below at 40 bar and 500C with a

volumetric flow rate of 90 m3/min. Steam exits the turbine at 20 bar and 400C. The steam is

then reheated at constant pressure to 500C before entering the second-stage turbine. Steam

leaves the second stage as saturated vapor at 0.6 bar. For operation at steady state, and

ignoring stray heat transfer and kinetic and potential energy effects, determine the (a) mass

flow rate of the steam, in kg/h, (b) total power produced by the two stages of the turbine, in

kW, (c) rate of heat transfer to the steam flowing through the reheater, in kW.

(Answers: a) 6.248 x 104 kg/h, b) 17565 kW, c) 3819 kW)


The figure below shows a solar collector panel embedded in a roof. The panel, which has a

surface area of 24 ft2, receives energy from the sun at a rate of 200 Btu/h per ft2 of collector

surface. Twenty-five percent of the incoming energy is lost to the surroundings. The remaining

energy is used to heat domestic hot water from 90 to 120F. The water passes through the

solar collector with a negligible pressure drop. Neglecting kinetic and potential effects,

determine at steady state how many gallons of water at 120F the collector generates per

hour. (Answer: 14.59 gal/hour)


Chapter 5: The Second Law of Thermodynamics


A power cycle operates between a reservoir at temperature T and a lower-temperature

reservoir at 280 K. At steady state, the cycle develops 40 kW of power while rejecting 1000

kJ/min of energy by heat transfer to the cold reservoir. Determine the minimum theoretical

value for T, in K. (Answer: 952 K)


A reversible heat pump cycle operates as in the figure below between hot and cold reservoirs

at TH = 27C and TC = 3C, respectively. Determine the fraction of the heat transfer QH

discharged at TH provided by (a) the net work input, (b) the heat transfer QC from the cold

reservoir TC. (Answers: a) 0.1, b) 0.9)

Chapter 6: Using Entropy


At steady state, work at a rate of 25 kW is done by a paddle wheel on a slurry contained

within a closed, rigid tank. Heat transfer from the tank occurs at a temperature of 250C to

surroundings that, away from the immediate vicinity of the tank, are at 27C. Determine the

rate of entropy production, in kW/K, (a) for the tank and its contents as the system, (b) for an

enlarged system including the tank and enough of the nearby surroundings for the heat

transfer to occur at 27C. (Answers: a) 0.0478 kW/K, b) 0.0833 kW/K)


Air enters an insulated turbine operating at steady state at 6.5 bar, 687C and exits at 1 bar,

327C. Neglecting kinetic and potential energy changes and assuming the ideal gas model,

determine (a) the work developed, in kJ per kg of air flowing through the turbine, (b) whether

the expansion is internally reversible, irreversible, or impossible.

(Answers: a) 393.53 kJ/kg, b) Irreversible)



The figure below shows a power system operating at steady state consisting of three

components in series: an air compressor having an isentropic compressor efficiency of 80%, a

heat exchanger, and a turbine having an isentropic turbine efficiency of 90%. Air enters the

compressor at 1 bar, 300K with a mass flow rate of 5.8 kg/s and exits at a pressure of 10 bar.

Air enters the turbine at 10 bar, 1400 K and exits at a pressure of 1 bar. Air can be modeled as

an ideal gas. Stray heat transfer and kinetic and potential energy effects are negligible.

Determine, in kW, (a) the power required by the compressor, (b) the power developed by the

turbine, and (c) the net power output of the overall power system.

(Answers: a) -2028 kW, b) 3690 kW, c) 1662 kW)

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MAAE3400 Problem Set 01