Sardar Vallabhbhai National Institute of Technology 2012 B.Tech Mechanical Engineering Thermodynamics - exam paper

(a)

A piston cylinder device operates 1 kg of fluid at 20 atm. pressure. The initial volume is 0.04 m³. The fluid is allowed to expand reversibly following a process pV¹-⁴⁵ =C, so that the volume becomes double. The fluid is then cooled at constant pressure until the piston comes back to the original position. Keeping the piston unaltered, heat is added reversibly to restore it to the initial pressure. Calculate the work done in the cycle.

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(b)

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When a system is taken from state a to state b along path acb, 84 kJ of heat flow into the system and the system does 32 kJ of work, (a) How much heat that flows into the system along path adb be, if the work done is 10.5 kJ? (b) When the system is returned from path b to a along the curved path, the work done on the system is 21 kJ. Does the system absorb or liberate heat, and how much of the heat is absorbed or liberated? (c) If U_a = 0 and Ud =42 kJ, find the heat absorbed in the processes ad and db.

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(c)

For a typical power plant producing 1200 MW of power the details are as under. Steam entering the turbine from boiler has 3333 kJ/kg of energy content. Energy rejected by the steam to the condenser is 2555 kJ/kg. Pumping work is 7 MW. Applying first law of thermodynamics, calculate the mass flow rate of steam in kg/sec and ultimately the capacity of boiler in TPH.

[5]

A housewife keep the door of a refrigerator dpen in order to beat the heat of summer by closing the door and window of a kitchen. However the cooling effect wears out with the passage of time and she feels uncomfortable with the raise of temperature. Assuming the plaster of a room is a good insulator and there is no heat exchange with the surrounding, how will you evaluate this case in the context of first law of thermodynamics?

[2]

t

^(e);

i

A domestic refrigerator is loaded with food and the door closed. During a certain period, the machine consumes 1 kW h of energy and the internal energy of the system drops by 5000 kJ. Find the net heat transfer for the system.

[3]

Attempt any two.

a

i

Find out the approximate temperature at which air will behave exactly as an ideal gas at low (but finite) pressure. The critical temperature for air is 133 K.

[2]

b

Write down Vander Waals equation of state and physical significance of major terms in it.

[2]

c

Derive the following expression for a reversible adial

RT;

^U2 ^U\ = , y-1

jatic process.

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[^Pl\ -¹ UJ

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[2]

A gas occupies 0.024m³ at 700 kPa and 95C. It is expanded in the non-flow process according to the law pv¹-² = constant to a pressure of 70 kPa after which it is heated at constant pressure work to its original temperature. Sketch the process on the p - v diagram, and calculate for the whole process the work done, the heat transferred, and the change of entropy. Take q> = 1.047 and c_v = 0.775 kJ/kg K for the gas.

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