2018-19
M.E.D., Z.H.C.E.T, A.M.U.
MEA-1110 (Engineering Thermodynamics)
Tutorial-2 (Unit – 2)
1. A cylinder closed by a frictionless leak proof piston contains a gas at a pressure of 150x103N/m2. The
cylinder area is 220 cm2. As the piston inwards, some of the gas is forced out of the cylinder through a
spring-loaded valve in the cylinder cover. An indicator connected to the cylinder shows that during this
process the pressure of the gas in the cylinder increases linearly with the piston position to 300 x103 N/m2.
Evaluate the work done at the piston face as the piston is pushed inwards a distance of 200 mm, when the
shape of piston crown (i.e. the surface exposed to the gas in the cylinder) is (a) flat, (b) hemispherical. [990 J]
2.
The following description is an idealization of the sequence of events which occur in the cylinder of a
reciprocating air compressor:
(a)
Initially, with the piston at it innermost position (inner dead-centre) and with the inlet and delivery valve shut,
the clearance volume contains air at the delivery pressure p2.
(b)
The piston move slowly outwards causing the clearance air to expand to the inlet pressure p1 according to pVn=
constant; p and V are respectively the pressure and volume of the clearance air at any instant during the process
and n is a constant.
(c)
When the pressure of the clearance air has fallen to p1, the inlet valve opens, and, as the piston completes its
outward stroke, atmospheric air is drawn into the cylinder. The pressure on the piston face is p1 throughout this
induction process.
(d)
With the piston in its outermost position (outer dead-centre), the inlet valve closes. The piston now commences
its inward stroke and compresses the air in the cylinder (i.e. the clearance air plus the induced air) according to
pVn= constant until its pressure rises to p2; p and V are respectively the pressure and volume of the air in the
cylinder during the comperission process.
(e)
When the pressure has risen to p2, the delivery valve opens and air is dischargeed at pressure p2 as the piston
completes its inward sroke.
(f)
Finally with the piston at the inner dead-centre the delivery valve closes leaving the clearance volume filled with
air at pressure p2. The sequence is then repeated.
All motions of the piston are assumed to be fully resisted. The clearance volume is ‘c’ percent of the swept
volume Vsw.
(i)
Sketch the indicator diagram.
(ii)
Deriven an expression for the net work done at the piston face per “cycle” in terms of p1, p2, Vsw, c and n.
Ans:
(iii)
Evaluate the net work per “cycle” when p2=600X103 N/m2 , p1=100X103 N/m2, Vsw=2.4 dm3, c = 5% and n = 1.2.
[-415 J]
1
(iv)
Evaluate the indicated power when the compressor speed is 390 rev/min assuming single-acting operation.
(Note that one complete sequence of events occurs during one revolution of the crankshaft) [-2.7 kW]
3.
A rigid body rests on a rough horizontal plane. A coil compression spring is atteched to the body with its axis
horizontal; the spring is such that a force of 4 N causes it to compress 10mm.
(a)
An agent applies a horizontal force to the free end of the spring causing the block to move slowly along the
table. When the block has moved a distance of 150 mm it comes into contact with a rigid stop fixed to the
surface of the table. During the motion the resisting forced the exerted by the plane on the block is 20 N. How
much work is done by agent ? [3.5 J]
(b)
If after the block has contacted the stop, the agent slowly relaxes the applied force, how much work will it have
done altogether ? [3.0 J]
(c)
How much work is done by the spring in (a) and in (a)+(b) ? [-0.5 J, 0]
4.
A mass of two kilograms of water at a temprature of 18 oC is poured into an insulated copper vessel which
initially is at a temprature of 15 oC. When the temprature have equalized, the water is at a temprature of 17.4
o
C. Determine the magnitude and sign of the heat transfer for each of the follwing three systems: (i) the vessel
and the insulation; (ii) the water; (iii) the vessel and the insulation plus the water. [5.02 kJ, -5.02 kJ, 0]
5.
The insulated copper vessel of problem 4. contains 10 kg of water at a temprature of 15 oC. A steel bar of mass
0.3 kg, at a temprature of 740 oC, is suddenly dropped into the water. When the temprature have equalized, the
temprature of the water is 17.4 oC. Determine the magnitude and sign of the heat transfer for each of the
following four systems: (i) the water; (ii) the vessel and the insulation; (iii) the steel bar; (iv) the vessl, the
insulation and the contents. [100.8 kJ, 5.02 kJ, -15.82 kJ, 0]
6.
A vertical cylinder fitted with a frictionless leakproof piston contains a quantity of gas. The piston is free to move
and its mass is such that the gas pressure is 200X103 N/m2; the upper surface of the piston is exposed to the
atmosphere. The gas executes a cycle by undergoing the following processes in sequence;
(i)
With the cylinder well-insulated, 1200 N m of stirring work are done on the gas by a paddle wheel projecting
through the cylinder wall. As a result the gas temprature rises and the piston move slowly upwards; the increas
in the gas volume is 2.80 dm3.
(ii)
With the insulation removed and the paddle wheel stationary, heat transfer from the gas restores the gas to its
initial state.
Evaluate:-(a) the displacement work and hence the net work done by the gas during process (i).
[560 J, -640 J]
(b) the net work done by the gas and the heat transfer from the gas in process (ii), [-560 J, 1200 J]
(c) the increase in energy of the gas in process (i) and in process (ii), [640 J, -640 J]
(d) the increasein energy of the gas for the combined process (i) plus (ii). [0 J]
7.
In an experiment to determine the mechanical equivalent of heat , a paddle wheel was fixed to the shaft of an
engine and rotated in water contained in a well-insulated closed vessel. The vessel was mounted freely on the
shaft and prevented from rotating by weights atteched to its side. At an engine speed of 270 rev/min it was
2
found that 173 kg of water had increased in temprature by 88 k in 51 min. The weights atteched to the vessel
exerted a force of 492 N at a distance of 1.5 m from the axis of rotation of the engine shaft. Sketch the
arrengement and evaluate the mechanical equivalent of heat. The heat transfer required to raise the
tempreture of 1 kg of water by 1 K is 4.19X103 J. [1, 63.79 MJ]
8.(a)
A system comprising 3 kg of a mixture of air and nitrogen is initially at a pressureof 100X103 N/m2 and a
temprature of 30 oC. The mixture undergoes a process to a pressure of 400X103 N/m2 and a temprature of 90 oC.
During the process the heat transfer from the mixture is 10 kJ and the work done on the mixture is 64000 N m.
Evaluate the increase in the energy of the mixture. [54 kJ]
(b)
Following the first process, the mixture undergoes a second process to a pressure of 100X103 N/m2 and a
temprature of 30 oC. The work done by the mixture during the second process is 50000 N m. Determine the
magnitude and the direction of the heat transfer during the second process, assuming that the specification of
the pressure and temprature fixes the state of the mixture completely. [-4 kJ]
(c)
What is the increase in the energy of the mixture after it has undergone both process in sequence? [0 J]
9.
A 100 mm-diameter vertical cylinder, closed by a piston, contains a combustible mixture at a temprature of 15
o
C. The piston is free to move and its mass is such that the mixture pressure is 240X103 N/m2; the upper surface
of the piston is exposed to the atmosphere. The mixture is ignited. As the reaction proceeds, the piston move
slowly upwards and heat transfer to the surroundings takes place. When the reaction is complete and the
temprature of the contents has been reduced to the initial value , 15 oC, it is found that the piston has moved
upwards a net distance of 85 mm and that the magnitude of the heat transfer to the surrounding is 4 kJ.
Evaluate the increase in the energy of the contents of the cylinder. [-4.16 kJ]
10. (a) A system consisting of a mixture of air and gasoline vapour at an initial temprature of 15 oC is contained in a rigid
vessel. The mixture undergoes the following processes in sequence.
(i)
The mixture tempature is raised to 200 oC by aheat transfer of +3 kJ.
(ii)
The mixture is ignited and burns completely; this process is adiabatic and tempratue rises to 1500 oC.
(iii)
The temprature of the products of combustion is reduced to 120 o C by a heat transfer of -32 kJ.
Evaluate the energy of the system after each process given that the initial energy of the system is 10kJ. [13, 13, -19 kJ]
(b)
An equal mass of the same mixture is contained in a cylinder closed by a piston. The mixture undergoes the
following process in sequence: (i) Adiabatic compression to a temprature of 200 oC.
(ii)
Adiabatic combustion at constant valume until burning is complete.
(iii)
Expansion to a temprature of 120 oC, the work done by the system being 31000 N m.
(iv)
Cooling at constant valume until the temprature is again 15 oC.
On the assumption that the energy of the system depends only on its temprature and chemical aggregation (i.e.
the way in which the elements are chemically combined), evaluate the work done during process (i) and heat
transfer during process (iii). Also state, with reasons, whether or not the system has excuted a cyclic process.
[-3 kJ, -1 kJ]
3
11. Four kilograms of carbon monoxide (CO) is contained in a rigid tank with a volume of 1 m 3. The tank is fitted with a
paddle wheel that transfers energy to the CO at a constant rate of 14 W for 1 hour. During the process, the specific
internal energy of the carbon monoxide increases by 10 kJ/kg. If no overall changes in kinetic and potential energy occur,
determine: (a) the specific volume at the final state, in m3/kg.
(b) the energy transfer by work, in kJ.
(c) the energy transfer by heat transfer, in kJ, and the direction of the heat transfer. [Ans: 0.25 m3/kg, 50.4 kJ, -10.4 kJ]
12. A desktop computer (Figure 1) is to be cooled by a fan whose flow rate is 0.34 m3/min. Determine the mass flow
rate of air through the fan at an elevation of 3400 m where the air density is 0.7 kg/m3. Also, if the average velocity of air
is not to exceed 110 m/min, determine the diameter of the casing of the fan.
Answers: 0.238 kg/min, 0.063 m]
Figure 1
Figure 2
13. The Figure 2 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 120 oF. 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 120 oF the collector generates per hour. Assume enthalpy h = c (T – To), where c =
0.999 Btu/lb.oF and specific volume at 120 oF = 0.0162 ft3/lb. [Answer: 145 gallons of water at 120 oF in 1 hour]
14. A gasoline engine has a specific fuel consumption of 0.3 kg/kWh. The stream of air and gasoline vapour, in the ratio
14:1 by mass, enters the engine at a temperature of 30 oC and leaves as combustion products at a temperature of 790
o
C. The net heat transfer rate from the fuel-air stream to the jacket cooling water and to the surroundings is 35 × 103 J/s.
The shaft power delivered by the engine is 26 kW. Evaluate the increase in the specific enthalpy of the fuel-air stream
assuming the changes in kinetic energy and in elevation to be negligible.
[Answer: -1877 kJ/kg]
15. Air flows through two turbine stages and an interconnecting
heat exchanger (Figure 3). A separate hot air stream passes in
counter-flow through the heat exchanger. Data are known at
various locations. Neglecting changes in velocities and elevation,
determine the temperature of the main air stream exiting the
heat exchanger and the power output of the second turbine.
For air, take Cp = 1005 J/kg K and assume that the enthalpy of air
is a function of temperature only.
Figure 3:
4