Ain Shams UniversityFaculty of EngineeringMechanical Power Dept.

Second Year Mech.2006t2007

Thermodvnamics II

SHEET (3)

1. 20 kg of liquid that has a specific heat of 0.8 kJ/kg K and an initial temperature of 50 'Cis poured into an insulated copper vessel of 4 kg and at 80 oC, After thermal equilibriumboth of the liquid and the copper vessel reach the final temperature. Assuming the specificheat of copper is 0.4 kJ/kg K. Compute the following:

a. The final temperature.b. Heat exchange between the liquid and the copper vesselc. The change of entropy during the processd. Is this process reversible or irreversible? Why?

2. A ngid tank has a volume t:.'4m3. It contains water at 300 kPa initially. A paddle inserledinto the water adds energy to the water until the water reaches 600 kPa, 200 'C.Determine;

a. The initial quality of the water.b. The mass of water in the tank.c. The work done on the water by the paddle.d. The change in entropy of the water during the process.e. Represent the process on P-v diagram.

3. For the steam power plant shown in the figure, the pressure and quality at various pointsin the cycle are given. Does this cycle satisfy the inequality of Clausius?

l5 kPa, 907o quality

0.7 MPa Saturated liquidCondense

15 kPa, 107o quality

4. A cylinder fitted with a frictionless piston contains steam at 300 oC, 2 MPa, at whichpoint the cylinher volume is 100L. The steam now expands, doing work against thepiston, until the final pressure is 300 kPa. How much work is done by the steam duringthis process, if the process is assumed to be reversible adiabatic?

5. A piston cylinder device contains 0.5 kg of saturated water vapour at200 oC. Heat is nowtransferred to steam, and steam expands reversibly and isothermally to a final pressure of800 kPa. Determine the heat transfer and the work done during the process.

0.7 MPa Saturated

6. A quantity of air undergoes a thermodynamic cycle consisting of three processes in series.Process 1-2: Constant-volume heating from pr = 0.1 MPa, tl = 15 oC, Vr = 0.02 m' toPz=0.42 MPa. Process 2-3: Constant-pressure cooling. Process 3-1: Isothermal heatingto the initial state. Employing the ideal gas model with Cp= 1 kJ/kg K, evaluate thechange in entropy for each process. Sketch the cycle on p-v and T-s coordinates.

7. 1.8 kg of gas having a volum-e of 1.5 m3 at 2.05 bar and.27 oC are compressedisentropically until the volume is reduced to one-third of the original, at this state thepressure is 8.56 bar. Find the value of the specific heats at constant volume and constantpressure.

8. Air is allowed to expand from an initial state A, where pa = 2.068 bar Ta = 333 K, to stateB, where Ps = 1.034 bar and Ts = 305 K. Calculate the change in the specific entropy ofthe air, and show that the change in the entropy is the same for:a) an isobaric process from A to some intermediate state C followed by an isovolumicchange from C to B, and,b) as isothermally change from A to some intermediate state D followed by an isentropicchange from D to B.

9. Steam enters a turbine at 2.0 MPa, 400 oC, expands in a reversible adiabatic process, andexhausts at l0 kPa. Changes in kinetic and potential energies are small between the inletand exit conditions of the turbine. The power output of this turbine is 800 KW. What isthe mass flow rate of steam through the turbine?

10. A cylinder fitted with a piston contains 3 kg of water at 500 KPa, 600 oC. The piston has'--' a cross-sectional area of O) m2 and is restrained by a linear spring (force proportional to

distance moved) with a spring constant of l0 kN/m. The system is now allowed to cooluntil the pressure inside drops to 150 kPa, as a result of transferring of heat to the room at20 'C. Calculate the net change of entropy, system and surroundings, for this process.

11. A valve connects two rigid tanks. Tank A is insulatedand contains 0.2 m3 of steam at 400kPa and 80 percent quality. Tank B is uninsulated and contains 3 kg of steam at 200 kPaand25O oC. The valve is now opened, and the steam flows from tank A to tank B until thepressure in the tank A drops to 300 kPa. During this process 600 kJ of heat is transferredfrom tank B to the surroundings at 0 oC. Assuming the steam remaining inside tank A tohave undergone a reversible adiabatic process, determine (a) the final temperature in eachtank and (b) the change of the universe entropy during this process.

12. Steam enters an adiabatic turbine at 6 MPa, 600 "C and 80 m/s and leaves at 50 kPa, 100oC and 140 m/s. If the power output of the turbine is 5 MW, determine: (a) the mass flowrate of the steam flowing through the turbine, and (b) the isentropic efficiency of theturbine.

13. Air enters an adiabatic compressor at 100 kPa and ll 'C atarate of I.2 m/s and exits at257 'C. The compressor has an isentropic efficiency of 84 percent. Neglecting thechanges in kinetic energy and potential energy, determine (a) the exit pressure and thepower required to drive the compressor.

14. A mass m of water at T1 is isobarically and adiabatically mixed with an equal mass ofwater at Tz. Show that the entropy change of the universe is

2mCnr,rf ]lijl/?-- "r" ' Jt Jr,

and prove that this is necessarily positive.

15. The temperature and pressure of an adiabatic air flow in a duct as registered at two pointsA and B were 400 K, 1 bar and 600 K, 2 bar, respectively. Determine the direction offlow.

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