Download thermodynamics, heat and mass transfer

THERMODYNAMICS, HEAT AND MASS TRANSFER
TUTORIAL NO: 3
FIRST LAW OF THERMODYNAMICS (CM)
1. During the working stroke of an engine the heat transferred out of the system was 150
kJ/kg of working substance. The internal energy also decreased by 400 kJ/kg of
working substance. Determine the work done and state whether it is work done on or
by the engine.
2. Air in a closed vessel of fixed volume 0.14 m3 exerts a pressure of 10 bar at 2500C. If
the vessel is cooled so that the pressure falls to 3.5 bar, determine the final
temperature and heat transfer.
3. A storage tank contains air at the same temperature as the surroundings (350C).
Suddenly it begins to rain, and the surrounding temperature drops to 200C. The tank
was initially at a pressure of 200 kPa, and the tank volume is 10 m3.
(a) What is the final pressure in kilopascals in the tank after the air cools in the tank
to the temperature of the surroundings?
(b) How much heat transfer in kilojoules occurred to or from the air during the
cooling? [R = 287 J/kg K, CV = 718 J/kg K]
4. A cylinder contains 1 m3 of a gas at 100 kPa and 1000C. The gas is compressed to a
volume of 0.25 m3, the final pressure being 600 kPa. Determine:
(a) the mass of gas
(b) the value of index n for compression
(c) change in internal energy of the gas. [R = 287 J/kg K, CV = 718 J/kg K]
5. Ethane initially at 35 kPa with a volume of 0.12 m3 is compressed frictionlessly in a
cylinder until its volume is halved in such a manner that its pressure and volume are
linearly related, P = a + b V. The final pressure is 80 kPa, and the change in internal
energy of ethane is 3.22 kJ. Determine the heat transfer.
6. Air (2 kg) is contained in a vertical frictionless piston-cylinder device shown in
Figure P3.6. The mass of the piston is such that the air has a pressure and temperature
of 10.0 MPa and 75.50C. There is a heat transfer to the cylinder until the piston
reaches some stops, at which point the total volume is 0.04 m3. There is an additional
heat transfer to the air until the pressure is 15.0 MPa. Determine the total heat transfer
and the total work, and show the process on a P-v diagram. [R = 287 J/kg K, CV =
718 J/kg K]
7. Shaft work (500 kJ/kg) is transferred to the air-filled frictionless piston-cylinder
device shown in Figure P3.7. Determine the heat transfer (kJ/kg). The initial and final
states of the air are T1 = 2000C, P1 = 400 kPa and T2 = 2500C, respectively. [CP =
1.005 kJ/kg K]
THERMODYNAMICS, HEAT & MASS TRANSFER
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TUTORIAL NO. 3
Figure P3.6
Figure P3.7
8. 1 kg of air can be expanded between two states as it does 20 kJ of work and receives
16 kJ of heat. A second kind of expansion can be found between the same initial and
final states which requires a heat input of only 9 kJ. What is the change of internal
energy in the first expansion, and what is the work done by the air in the second
expansion?
9. The following table gives data, in kJ, for a system undergoing a thermodynamic cycle
consisting of four processes in series. For the cycle, kinetic and potential energy
effects can be neglected. Determine:
(a) the missing table entries, each in kJ.
(b) whether the cycle is a power cycle or a refrigeration cycle.
Process
1-2
2-3
3-4
4-1
U
----670
--- 360
Q
----0
----
W
- 610
230
920
0
10. A gas is held in a cylinder behind a piston undergoes a cycle composed of three
process:
Process 1 – 2: an adiabatic compression process. For this process W1-2 = - 58 kJ.
Process 2 – 3: an expansion during which heat is added and work is done on the
piston. Q2-3 = 253 kJ; and W2-3 = 95 kJ.
Process 3 – 1: a cooling of the gas while the piston is stationary to bring the gas to its
initial state.
Determine the net heat transfer and heat transfer of process 3 – 1.
ANSWER
1.
2.
3.
4.
5.
6.
7. – 449.8 kJ/kg
8. – 4 kJ, 13 kJ
9. 610 kJ, 0, 900 kJ, - 920 kJ, - 360 kJ
10. 37 kJ, - 216 kJ
250 kJ/kg
183 K, - 228 kJ
190.3 kPa, - 243.7 kJ
0.934 kg, 1.292, 435.54 kJ
– 0.23 kJ
1201 kJ, 200 kJ
THERMODYNAMICS, HEAT & MASS TRANSFER
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TUTORIAL NO. 3