UNIVERSITY OF TORONTO

FACULTY OF APPLIED SCIENCE AND ENGINEERING

FINAL EXAMINATION, APRIL 2018

MIE 311H1 S - THERMAL ENERGY CONVERSION

Exam Type: X

Examiner: J.S. Wallace

You may use your copy of the course textbook by Moran and Shapiro, your lab manual, class

notes or study notes prepared by you personally, returned problem sets, material distributed in

class and any printed/written material posted on the Winter 2018 MIE 311 course

Blackboard. Calculators will be non-printing, non-communicating, silent & self-powered. Show

your work on your exam booklet.

1. (20%) A number of electric vehicles are now available with a "range-extender" gasoline

engine. The engine drives an electrical generator, not the wheels, and is only intended to

recharge the battery while on the road. A good example is the range extender engine in the

BMW i3. It is a 2 cylinder engine having a bore and stroke of 79 mm and 66 mm respectively and

a compression ratio of 10.6:1.

Assume that this engine can be modeled as an air-standard Otto cycle with a heat input of 0.883

kJ/cycle. Intake air temperature and pressure are 100 kPa and 47°C respectively. Due to the

large temperature range involved, the variation of specific heat with temperature cannot be

neglected so the Air Tables must be used. Rair = 0.287 Id/kg-K

Calculate the clearance volume (m3) in one cylinder

Calculate the mass of air (kg) in one cylinder.

Calculate the temperature T2 (K) and pressure P2 (kPa) at the end of the compression stroke.

Calculate the temperature T3 (K) and pressure P3 (kPa) at the end of the heat addition.

(continued next page)

Page 1 of

1 (Continued)

Calculate the temperature 14 (K) and pressure P4 (kPa) at the end of the expansion stroke.

Calculate the net work output, Wnet (ki), and the thermal efficiency for the cycle

Calculate the mean effective pressure (kPa) for the cycle.

Calculate the power output (kW) of this engine running at 5000 rpm at the operating

conditions used in (a) through (g).

2. (20%) Refrigerant 134a enters the compressor of a vapor compression refrigerator as

superheated vapor at 0.14 MPa and -10°C at a rate of 0.12 kg/s, and it leaves the compressor at

0.7 MPa and 50°C. The refrigerant is cooled in the condenser to a saturated liquid state at 24°C

and then throttled to 0.15 MPa.

Condenser

3

Expansion Compressor valve WCOMP

Evaporator

Qevap

What is the pressure drop across the condenser and the evaporator respectively?

Show the cycle on a 1-S diagram (sketched in your exam booklet) with respect to the

saturation lines

Calculate the rate of heat removal Qe-L,ap from the refrigerated space

Calculate the actual power input Wcomp to the compressor

Calculate the isentropic efficiency rjcomp of the compressor

Calculate the coefficient of performance P of the refrigerator

Page 2 of 4

3. (20%) Nitrogen and hydrogen are mixed in a steady-flow adiabatic device in a ratio of 4 Ibm

hydrogen per Ibm nitrogen. The hydrogen enters at 20 psia, 100°F and the nitrogen at 20 psia,

500°F. The pressure after mixing is 18 psia. Assuming ideal gas behavior, determine:

the mass fractions and mole fractions of N2 and H2 after mixing

the exit temperature, and

(b) the entropy production per Ibm of mixture.

Useful data:

RH2 = 0.98512 BTU/IbmR, RN2 = 0.07090 BTU/lbmR

MH2 = 2.016 Ibm/lbmoie, MN2 = 28.014 lbm/lbmoie

Nitrogen Hydrogen

Temperature (°F) cp (BTU/IbmR) Cv (BTU/lbmR) Cp (BTU/lbmR) Cv (BTU/lbmR)

40 0.248 0.177 3.397 1.409

100 0.248 0.178 3.426 1.404

200 0.249 0.178 3.451 1.399

300 0.250 0.179 3.461 1.398

400 0.251 0.180 3.466 1.397

500 0.254 0.183 3.469 1.397

4. (20%). Two moisture containing air flows are mixed in an adiabatic and steady-flow process.

The first flow enters at 32°C and 40% relative humidity at a volumetric flow rate of 20 m 3/min

and the second flow enters at 12°C and 90% relative humidity at a volumetric flow rate of 25

MI/min. The overall pressure is constant throughout the process at 101.325 kPa.

Determine using an analytical solution (not the psychrometric chart):

The mass flow rates of air: iñ, in2, and 7n3

The specific humidity (03 at the exit

The dry bulb temperature 13 at the exit

The relative humidity at the exit

Useful constants for Q4: Mair = 28.97 kg/kg-mole, Mwater18.016 kg/kg-mole, Runiversal = 8.314

Id/kg-mole-K, Rair = 0.2870 Id/kg-K, Rwater = 0.4414 Id/kg-K, cp,air= 1.005 Id/kg-K

Page 3 of 4

S. (20%). A Rankine cycle power plant powered by a low-temperature nuclear source has been

proposed for operation in the Artic. This proposed power plant, shown in the figure below left,

uses carbon dioxide (CO2) as a working fluid. The boiler pressure is 1100 psia (the boiler is the

"heater" in the diagram), which as the T-s diagram below right shows, is higher than the critical

pressure for carbon dioxide, which makes it a supercritical Rankine cycle. The critical pressure

and temperature for carbon dioxide are 1071.3 psia and 87.56°F respectively. The carbon dioxide

leaving the boiler is at 200°F (13). The condenser operates at -40°F (Psat = 145.77 lbf/in2 @ -400F).

The pump and turbine have efficiencies of 50% and 85% respectively. The power plant needs to

deliver a new power output of 2 kW (1 kW = 3412 BTU/hr).

Pump

t

Turbine

+ Gondeser

Thermodynamic properties of carbon dioxide can be obtained from the Pressure-Enthalpy

diagram attached (Figure A.1OE from your textbook).

Determine for the proposed power plant:

the actual specific turbine work, Wt,a (BTU/Ibm)

the actual specific pump work, Wp,a (BTU/Ibm)

the actual specific net work, wnet (BTU/Ibm)

the mass flow rate TflCO2 (lbm/hr) of CO2 required.

The required heat input H (BTU/hr) from the nuclear source

The energy conversion efficiency (q) for this power plant.

Show the actual process on the P-h diagram (Put you name and student number on the P-h

diagram and place it inside your exam booklet when you submit your exam).

Page 4 of 4

40 0 40 80 4000

2000

1000

200

100

60

\Carbon Diox:

NX

vw

CIO

cq

Ii ) / /

/ L

___ J_LLLLi r 80'i \'\ \

0

120 160 280 240 280 4000

2000

1000

800

600

400

200

100

80

Carbon dioxide P-h diagram for question 5. Name Student number

60 60

40 0 40 80 128 160 200 240 280

ENTHALPY. Btu/lb .

for pdL 1 ilih \I Il1I. \l I R, 1 1k lHik 11' Ii