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UNIVERSITY OF MALTA FACULTY OF ENGINEERING

B.ENG.(HONS.) IN MECHANICAL ENGINEERING YEAR I SEMESTER II

MAY/JUNE 09 SESSION OF EXAMINATIONS

MEC 1405 Thermodynamics I 23rd June 2009

0915 1215 hours

This paper contains SIX questions. You are to attempt FIVE.

Stationery: Use of calculators is allowed Psychrometric Chart to be available Steam Tables

1. (a) Write down the non-flow and flow energy equations. (4 marks)

(b) A steam turbine receives a steam flow of 1.35 kg/s and the power output is 500 kW. The heat loss from the casing is negligible.

Calculate: (i) the change of specific enthalpy across the turbine when the velocities at

entrance and exit and the difference in elevation are negligible;

(ii) the change of specific enthalpy across the turbine when the velocity at entrance is 60m/s, the velocity at the exit is 360m/s and the inlet pipe is 10m above the exhaust pipe.

If the steam inlet conditions are 50 bar and 500oC, what is its specific enthalpy at the inlet. Hence calculate the specific enthalpy at the exit for conditions (i) and (ii) above.

(16 marks)

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2. (a) A bicycle pump which has a stroke of 20 cm is used to force air into a tyre against a pressure of 4 bar. What length of stroke will be swept through before air begins to enter the tyre when the piston is pushed in i) slowly and (ii) quickly? Assume that the atmospheric pressure is 1 bar.

(10 marks)

(b) A closed system receives 168.7 kJ of heat at constant volume. It then rejects 177 kJ of heat while 40 kJ of work is done on it at constant pressure. If an adiabatic process can be found which will restore it to its initial state, how much work will be done by the system during that process? If the value of internal energy in the initial state is arbitrarily put equal to zero find the internal energies at the other two states. Draw the cycle on a p-v diagram.

(10 marks)

3. A mass of 2 kg of steam is initially at a pressure of 3 bar. The initial dryness fraction is such that when the steam has been heated at constant volume to 4 bar it is saturated. After this heating process the steam is compressed isentropically to 10 bar.

Find the initial dryness fraction, the final temperature and the heat and work transfers for the processes. Sketch the processes o a T-s and p-v diagrams.

(20 marks)

4. (a) Show that for a polytropic process the change of entropy between two states for an ideal gas is given by:

+

=

2

1

1

212 lnln p

pRTT

css p

(8 marks)

(b) Two vessels, one exactly twice the volume of the other, are connected by a valve and immersed in a constant temperature bath of water. The smaller vessel contains hydrogen (molar mass 2 kg/kmol), and the other is completely evacuated. Calculate the change of entropy per kilogram of gas when the valve is opened and conditions are allowed to settle. Sketch the process on T-s and p-v diagrams. Assume hydrogen to be a perfect gas.

(12marks)

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5. (a) Show that:

ivi

v cm

mc = and ip

ip c

m

mc = .

(6 marks)

(b) A vessel of 4 m3 capacity contains a mixture of nitrogen (N2, molar mass 28 kg/kmol) and carbon dioxide (CO2, molar mass 44 kg/kmol), the analysis by volume showing equal quantities of each. The temperature of the mixture is 20oC and the total pressure is 5bar. Determine the mass of each constituent.

(9 marks)

(c) By referring to the psychrometric chart provided, what is the enthalpy, specific volume and percentage saturation of air with a dry bulb temperature of 30oC and wet bulb temperature of 20oC. Mark this point clearly on the chart. If the air is cooled to 25oC dry bulb and 50 percent saturation what is the associated enthalpy drop.

(5 marks)

6. In a mixture of methane (CH4) and air there are three volumes of oxygen to one volume of methane. From initial conditions of 1 bar and 95 oC the gas is compressed reversibly and adiabatically through a volume ratio of 5. Assuming that air contains only oxygen and nitrogen, and referring to table of values at the end of this exam paper, calculate:

(a) the values of cp , cv , R and for the mixture;

(b) the final pressure and temperature of the mixture

(c) the work input per unit mass of mixture (20 marks)

Additional information ( )

1)(

1121122

=

=

n

TTRn

vpvpW where W is specific work, p is pressure and v specific

volume, n is the polytropic index, R is the specific gas constant and T is the temperature. Subscripts 1 and 2 refer to the states.

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