Department of Mechanical Engineering
Assignment Problem Sheet 1
(Engineering Thermodynamics) MEC2103
1. Air at 0.02 m3 at 200 kPa and 30°C is compressed to 1/10 th of its initial volume. The process obeys the law PV1.3 = constant.
What is the final temperature and work done in the process?? [Ans. 331.5°C]
2. 2 kg of a gas is contained in a piston-cylinder assembly at initial conditions of 2 m 3 and 100 kPa. The gas is allowed to expand to
a final volume of 5 m3. Determine the amount of work done for the following processes:
(a) pressure remains constant, (b) isothermal process, (c) PV2 is constant.
[Ans (a) 300 kJ, (b) 183.26 kJ, (c) 120kJ)]
3. The piston of an oil engine of area 0.0045 m2, moves downwards by 75 mm, drawing in 0.00028 mm 3 of fresh air from the
atmosphere. The pressure in the cylinder is uniform at 80 kPa during the process while the atmospheric pressure is 101.325 kPa,
the difference being due to the flow resistance in the induction pipe and the inlet valve. Estimate the displacement work done by
the air in the cylinder. [Ans: 27 J]
4. An engine cylinder has a piston of area 0.12 m 2 and contains gas at a pressure of 1.5 MPa. The gas expands according to a
process which is represented by a straight line on the pressure-volume diagram. The final pressure is 0.15 MPa. Calculate the
work done by the gas on the piston if the stroke length is 0.30 m. [Ans: 29.7 kJ]
5. A mass of gas is compressed in a quasi-static process from 80 kPa, 0.1 m3 to 0.4 MPa, 0.03 m3. Assuming that the pressure and
volume are related by PVn = constant, find the work done by the gas system. [Ans: -11.83 kJ]
6. At the beginning of the compression stroke of a two-cylinder internal combustion engine, the air is at a pressure of 101.325 kPa.
Compression reduces the volume to a fifth of the original volume, and the law of compression is given by PV1.2 = constant. If the
bore and stroke of each cylinder is 0.15 m and 0.25 m respectively, determine the power absorbed in kW by compression strokes
when the engine speed is such that each cylinder undergoes 500 compression strokes per minute. [Ans: 17.72 kW]
7. Determine the total work done by a gas system following an expansion process as shown in the figure below:
[Ans: 2.251 MJ]
8. A system of volume V contains a mass m of a gas at pressure P and temperature T. The macroscopic properties of the system
obey the following relationship.
, where a, b and R are constants. Obtain an expression for the displacement work done by the system
during a constant temperature expansion from volume V1 to a volume V2. Calculate the work done by the system which contains
10 Kg of this gas expanding from 1 m3 to 10 m3 at a temperature of 293 K. Use the values: a = 15.7x104 Nm4, b = 1.07x10-2 m3
and R = 0.278 kJ/kg.K. [Ans: 1742.14 kJ]
9. An elastic sphere initially has a diameter of 1 m and contains a gas at a pressure of 1 atmosphere. Due to heat transfer, the
diameter of the sphere increases to 1.1 m. During the heating process the gas pressure inside the cylinder is proportional to the
sphere diameter. Calculate the work done by the gas. [Ans: 18.4 kJ]
10. A piston-cylinder device contains 0.05 m3 of a gas initially at 200 kPa. At this state, a linear spring having a spring constant of
150 kN/m is touching the piston but exerting no force on it. Now heat is transferred to the gas, causing the piston to rise and to
compress the spring until the volume inside the cylinder doubles. If the cross-sectional area of the piston is 0.25 m2, determine
(a) the final pressure inside the cylinder, (b) the total work done by the gas and (c) the work done against the spring to compress
it. [Ans: 320 kPa, 13 kJ, 3 kJ]
