ChE Thermo Problems

Question 1

Determine for a unit mass of air, the change in enthalpy when heated from zero°C to 100°C if:
i. Cp = 1 kJ/kg-K constant
H= 100 kJ/kg

ii. Cp = 0.95 + 0.00002T – 0.03x10-6 T2
H= 96.09 kJ/kg

Answer 1

100 kJ/kg; 96.09 kJ/kg

Question 2

An insulated, constant-volume system containing
1.36 kg of air receives 53 kJ of paddle work. The
initial temperature is 27°C. Determine
a) The change of internal energy.
U= + 53 kJ

b) The final temperature
Assume a mean value Cv = 0.718 kJ/kg-K
T= 81.3°C

Answer 2

+ 53 kJ; 81.3°C

Question 3

Determine using Steam Tables, the volume occupied by 2 kg of steam at 500 kPa, under the
following conditions and specify the state of steam.

a) Pure liquid state
V= 0.00218 m3

b) When it is in a pure vapour state
V= 0.7498 m3

Answer 3

0.00218 m3; 0.7498 m3

Question 4

A nuclear reactor generates 3000 MW of heat. The
heat is transferred in a heat exchanger of energy
transfer efficiency 75% into steam which is expanded in a turbine in order to produce a power output. The steam is condensed in a condenser,
releasing 1800 MW of heat, and pumped back through the heat exchanger by a feed pump which requires 3% of the power output from the turbine.
Determine:
a) The net power output from the plant.
P= 463.9 MW

b) The power output from the turbine.
P= 450 MW

Answer 4

463.9 MW; 450 MW

Question 5

A boiler receives feed water at 40°C and delivers steam at 2 MPa and 500°C. if the furnace is oil fired, the calorific value of oil being 42000 kJ/kg and
4000 kg oil are burned while 45000 kg of steam are produced, determine:

a) The heat supplied in the boiler.
Q= 1.484x10^8 kJ

b) The efficiency of the boiler.
e= 88%

Assume the values of enthalpies at the two state points as:
h1 = hf@40°C = 169.33 kJ/kg at 2 MPa, 500°C, h2 = 3467.6 kJ/kg

Answer 5

1.484x10^8 kJ; 88%

Question 6

A motorist equips his automobile tyres with a relieftype valve so that the pressure inside the tyre will never exceed 220 kPa (gauge). He starts the trip with a pressure of 200 kPa (gauge) and a temperature of 23°C in the tyres. During the long drive the temperature of the air in the tyres reaches 83°C. each tyre contains 0.11 kg of air. Determine the mass of air escaping each tyre

m= 0.0094 kg

Answer 6

0.0094 kg

Question 7

Determine the pressure of water vapour at 300°C, if its specific volume is 0.2579 m3/kg, using the following method:
a) Ideal gas equation
P= 1.025 MPa

b) Van-der-Waals equation
P= 1.006 MPa

Answer 7

1.025 MPa; 1.006 MPa

Question 8

Oxygen has a molecular weight **of 32 and a specific heat at constant pressure of 0.91 kJ/kgK.
a) Determine the ratio of the specific heats.
n= 1.4

b) Calculate the change in internal energy and
enthalpy if the gas is heated from 300 to 400 K
U= 65 kJ/kg, H= 91 kJ/kg

Answer 8

1.4, 65 kJ/kg, 91 kJ/kg

Question 9

Calculate the density of Ethane at 171 bar and 458K; assume for Ethane:
TC = 305 K
PC = 48.80 bar
R = 319.3 J/kg-K

a) Assume it behaves as a perfect gas.
density= 117 kg/m3

b) Using the compressibility chart.
Z= 146 kg/m3

Answer 9

117 kg/m3, 146 kg/m3

Question 10

You have a 200 gram cup of coffee at 100°C, too
hot to drink. How much will you cool it by adding 50 gm
of water at 0°C?

Answer 10

80°C

Question 11

An ideal gas occupies a volume of 0.5 m3 at a temperature of 340 K and a given pressure. The gas undergoes a constant pressure process until the
temperature decreases to 290 K. Determine
a) The final volume.
V= 0.426 m3

b) The work if the pressure is 120 kPa.
W= -8.88 kJ

Answer 11

0.426 m3; -8.88 kJ

Question 12

A reciprocating internal combustion engine has a
clearance volume of 0.0001 m3 and a compression ratio (volume ratio) of 10. The pressure and temperature of the combustion gases when the piston is at top dead centre are 4000 kN/m2 and 1800°C respectively. Assuming that the expansion process follows PV^1.3 = constant, calculate:

a) The work transfer in this process; and
W= 66.7 J

b) The temperature of the gases at the end of the
process
T= 1039 K

Answer 12

66.7 J; 1039 K

Question 13

An ideal centrifugal air compressor takes in air at 1
bar, 15°C and compresses it reversible and adiabatically to a pressure of 4 bar.

a) Calculate the delivery temperature of the gas.
T= 428 K

b) If kinetic energy and potential energy changes
are negligible calculate the specific work transfer in the compression process.
W= -140.7 kJ/kg

Answer 13

428 K; -140.7 kJ/kg

Question 14

Milk initially at 30°C is to be kept in a chilled tank at 5°C. If the total volume of milk is 100 litres, its density is 1100 kg/m3 and the specific heat capacity
of 4.2 kJ/kg-K. Determine the heat extraction rate assuming the chiller to be perfectly insulated.

Q= 11.55 kW

Answer 14

11.55 kW

Question 15

Self-ignition would occur in the engine using certain brand of petrol if the temperature due to compression reached 350°C. Calculate the highest ratio of compression that may be used to avoid preignition if the law of compression is PV^1.3 = c .

r= 11.36

Answer 15

11.36

Question 16

A boiler receives feed water at 20 kPa as saturated liquid and delivers steam at 2 MPa and 500oC. If the furnace of this boiler is oil fired, the calorific value of oil being 42000 kJ/kg determine the efficiency of
the combustion when 4.2 tonnes of oil was required
to process 42000 kg of steam.

96%

Answer 16

96%

Question 17

2 kg of air is heated at constant pressure of 2 bar to
500oC. Determine the change in its entropy if the
initial volume is 0.8 m3.

S= 2.04 kJ/K

Answer 17

2.04 kJ/K

Question 18

Find the specific volume for H2O at 10 MPa and 500°C using:
a) Compressibility chart;
V= 0.032 m3/kg

b) Steam tables
V= 0.03279 m3/kg

Answer 18

0.032 m3/kg; 0.03279 m3/kg

Question 19

10 kg/s steam at 6 MPa and 500oC, expands isentropically in a turbine to a pressure of 100 kPa. If the heat transfer from the casing to surroundings represents 1 per cent of the overall change of
enthalpy of the steam, calculate the power output of
the turbine. Assume exit is 5 m above entry and that initial velocity of steam is 100 m/s whereas exit velocity is 10 m/s.

96%

Answer 19

96%

Question 20

Determine the volume for carbon dioxide contained
inside a cylinder at 0.2 MPa, 27°C:-
a) assuming it behaves as an ideal gas
b) taking into account the pressure and
volume associated with its molecules

V= 0.2833 m3/kg

Answer 20

0.2833 m3/kg

Question 21

Self-ignition would occur in an engine using certain brand of petrol if the temperature due to compression reaches 350°C; when the inlet condition is 1 bar, 27°C. Calculate the highest compression ratio possible in
order to avoid self-ignition, if the compression is according to
a) Adiabatic, with index of 1.4; n= 6.2

b) Polytropic, with index of 1.3
n= 11.4

Answer 21

6.2; 11.4

Question 22

Air at 27°C receives heat at constant volume until its temperature reaches 927°C. Determine the heat added per kilogram? Assume for air Cv = 0.718 kJ/kg-K

Q= 646.2 kJ/kg

Answer 22

646.2 kJ/kg

Question 23

** In a non-flow process there is heat transfer loss of 1055 kJ and an internal energy increase of 210 kJ. Determine the work transfer and state whether the process is an expansion or compression.

W= -1265 kJ, compression

Answer 23

-1265 kJ, compression

Question 24

**An unknown gas has a mass of 1.5 kg contained in a bottle of volume 1.17 m3 while at a temperature of 300K, and a pressure of 200 kPa.

Determine the ideal gas constant and deduce the gas?
R = 520 J/kg-K;
M = Ro/R = 15.99]

Answer 24

R = 520 J/kg-K; M = Ro/R = 15.99]

Question 25

Steam (0.05 kg) initially saturated liquid, is heated
at constant pressure of 0.2 MPa until its volume becomes 0.0658 m3. Calculate the heat supplied during the process.

Q= 128.355 kJ

Answer 25

128.355 kJ

Question 26

Steam at 4 MPa, 400oC expands at constant entropy
till its pressure is 0.1 MPa.
Determine:
a) the energy liberated per kg of steam
758 kJ/kg

b) repeat if the process is 80% isentropic
606 kJ/kg

Answer 26

758 kJ/kg, 606 kJ/kg

Question 27

**The gas in an internal combustion engine, initially at a temperature of 1270°C; expands polytropically to five times its initial volume and one-eight its initial pressure. Calculate:

a) The index of expansion, n,
n= 1.292

b) The final temperature
T= 698K

Answer 27

1.292; 698K

Question 28

A mass of air at 330°C, contained in a cylinder
expanded polytropically to fuve times its initial volume and 1/8th its initial pressure which is 1 bar. Calculate:
a) The value of the expansion index;
n= 1.292

b) The work transfer per unit mass.
W= +222 kJ

Answer 28

1.292; +222 kJ

Question 29

A 6 m3 tank contains helium at 400K is evacuated form atmospheric pressure of 100 kPa to a final pressure of 2.5 kPa. Determine
a) The mass of helium remaining in the tank;
m= 0.018 kg

b) The mass of helium pumped out;
m= 0.704 kg

Answer 29

0.018 kg; 0.704 kg

Question 30

A closed rigid container has a volume of 1 m3 and holds air at 345 kPa and 20°C. heat is added until the temperature is 327°C. determine the change in Internal energy using an average value of the specific heat

U= 932 kJ

Answer 30

932 kJ

Question 31

Steam is expanded isentropically in a turbine from
30 bar and 400°C to 4 bar. Calculate the work done
per unit mass flow of steam. Neglect changes in Kinetic and Potential energies.

W= 476 kJ/kg

Answer 31

476 kJ/kg

Question 32

Find the specific volume for H20 at 1000 kN/m2 and
300°C by using:
a) the ideal gas equation assuming R = 461.5 J/kg
K
V= 0.264 m3/kg

b) steam tables
V= 0.258 m3/kg

Answer 32

0.264 m3/kg, 0.258 m3/kg

Question 33

The cylinder of an engine has a stroke of 300 mm and a bore of 250 mm. The volume ratio of
compression is 14:1. Air in the cylinder at the beginning of compression has a pressure of 96 kN/m2 and a temperature of 93°C. The air is compressed for the full stroke according to the law PV1.3 = C. Determine the work transfer per unit mass of air. Assume air R = 287 J/kg-K.

W= -424 kJ/kg

Answer 33

-424 kJ/kg

Question 34

An air compressor receives air at 27°C and delivers it to a receiver at the rate of 0.5 kg/s. It is driven by an electric motor which absorbs 10 kW and the fficiency of the drive is 80%. Water jacket cooling
is used at the rate of 6 kg/min while its temperature rises from 10°C and 20°C. Estimate the temperature of the air delivered.
Data: Cpw = 4.186, and Cpa = 1.005 kJ/kg-K

T= 43.5°C

Answer 34

43.5°C

Question 35

A burner heats air from 20 to 40°C at constant pressure. Determine the change in entropy for a unit
mass of air going through the heater, assuming that
for air Cp = 1 kJ/kg-K.

S= 0.03356 kJ/kg-K

Answer 35

0.03356 kJ/kg-K

Question 36

Air is expanded isentropically in a nozzle from 13.8 bar and 150°C to a pressure of 6.9 bar. The inlet velocity to the nozzle is very small and the process occurs under steady-flow, steady-state conditions.
Calculate the exit velocity from the nozzle knowing that the nozzle is laid in a horizontal plane and that the inlet velocity is 10 m/s.

v= 390.9 m/s

Answer 36

390.9 m/s

Question 37

In a non-flow process carried out on 5.4 kg of a substance, there was a specific internal energy decrease of 50 kJ/kg and a work transfer from the
substance of 85 kJ/kg. Determine the heat transfer
and state whether it is gain or loss.

Q= 189 kJ, gain

Answer 37

189 kJ, gain

Question 38

The model ‘6SE-TCA3 Perkins’ diesel engine have a stroke of 190 mm and a bore of 160 mm. If its clearance volume is 5% of the swept volume, determine the pressure and temperature at the end of compression when the inlet condition is 1 bar, 27°C. Assume n = 1.38

P= 67.2 bar;
T= 956K

Answer 38

67.2 bar; 956K

Question 39

A closed rigid system has a volume of 85 litres contains steam at 2 bar and dryness fraction of 0.9. Calculate the quantity of heat which must be
removed from the system in order to reduce the pressure to 1.6 bar.

Q= -38 kJ

Answer 39

-38 kJ

Question 40

A piston and cylinder mechanism contains 2 kg of a
perfect gas. The gas expands reversibly and
isothermally from a pressure of 10 bar and a
temperature of 327°C to a pressure of 1.8 bar.
Calculate:
a) The work transfer;
W= 617 kJ

b) The heat transfer and;
Q= 617 kJ

Answer 40

617 kJ; 617 kJ