## Basic Thermodynamics - Jan 2013

### Mechanical Engineering (Semester 3)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1 (a)** Define the following examples:

(i) Open system

(ii) Closed system

(iii) Path function

(iv) Point function (8 marks)
**1 (b)** Distinguish between:

(i) Intensive and extensive properties

(ii) Thermal equilibrium and mechanical equilibrium

(iii) Microscopic and macroscopic point of view.(6 marks)
**1 (c) ** State zeroth law of themodynamics. The temperature, t on a certain scale is defined in terms of the thermometric property X be the relation t=a ln x+b where a abd b are constants. On this scale the temperature of ice and steam points are 0 and 100, respectively. Experiments reveal that X_{i}=1.86 and X_{s}=6.81. FInd the temperature for an X value of 3.2 on this thermometer.(6 marks)
**2 (a)** List the similarities between heat and work.(4 marks)
**2 (b)** State and explain thermodynamic definition of work(4 marks)
**2 (c) ** Derive the expression for the displacement work in resisted polytropic process. (PV^{n}= Constant).(6 marks)
**2 (d)** A certain mass of air is compressed from 1 bar, 0.1 m^{3} to 6 bar in a piston cylinder device according to PV^{1.4} = constant. Find the work of compression for air. Had the compression been carried out hyperbolically between the same initial state and the same final pressure as above what would be the work done on air?(6 marks)
**3 (a)** State and explain the first law of thermodynamics. Give its equation with reference to a cyclic and non-cyclic process.(6 marks)
**3 (b) ** A fluid confined in a cylinder by spring loaded, frictionless piston so that the pressure in the fluid is linear function of the volume (P=a+bV). The internal energy of the fluid is given by the following equation:

U=34+3.15 PV

Where U is kJ, p in kPa and V in cubic metre. if the changes from a initial state of 170 kPa, 0.03 m^{3} to a final state of 400 kPa, 0.06 m^{3}, with no work other than that done on the piston, find the direction and magnitude of the work heat transfer.(8 marks)
**3 (c) ** Steam at a rate of 0.42 kg/s and enthalpy of 2785 kJ/kg and a velocity of 33.3 m/s s supplied to steadily operating turbine. The steam leaves the turbine at 100 m/s and an enthalpy of 2512 kJ/kg. The inlet pipe is 3 m above the exit pipe. Rate of heat loss from the turbine casing is 0.29 kJ/s. What is the power output of the turbine?(6 marks)
**4 (a)** Why are engineers interested in reversible processes even thrigh they can never be achived?(2 marks)
**4 (b)** Define reversible engine. Show that of all the reversible heat engine working between any two constant but different thermal reservoir temperatures, the reversible reversed beat engine will have the maximum COP.(8 marks)
**4 (c) ** A Carnot engine receives heat at 750 K and rejects the waste heat to the enviornment at 300K. The entire output of the heat engine is used to drive a Carnot refrigerator that removes heat from the cooled space at -15°C at a rate of 400 kJ/min and rejects to the same environment at 300K. Determine the (i) the rate of heat supplied to the heat engine (ii) The total rate of heat rejection to the environment.(10 marks)
**5 (a)** Define inequality of Clausius and entropy of a system. Show that for an irreversible process ds ? ?Q/T.(10 marks)
**5 (b)** 1.5 kg of air initially at 25°C is heated reversibly at constant pressure until volume is double and heated reversibly until pressure is double at constant volume. For the total path. Determine (i) the work transfer (ii) the heat transfer and (iii) the change in entropy(10 marks)
**6 (a)** Sketch the T-P phase diagram for water. Mark on it the following: solid region, liquid region, vapour phase, triple point and critical point.(5 marks)
**6 (b)** State whether the following samples of steam are wet, dry or superheated. Justify your answer. (i) Pressure=1 MPa absolute, enthalpy=2880 kJ.kg, (ii) Pressure=500 kPa absolute, volume=0.35m^{3}/kg (iii) Temperatur=200°C, Pressure=1.2 MPa (iv) Temperature = 100°C, entropy=6.88 kJ/kg K (v) Pressure=10 kPa, enthalpy=2584.8 kj/kg.(5 marks)
**6 (c) ** 0.1 kg saturated steam expands reversibly from 10 to 1 bar in a piston-cylinder device according PV^{1.3}=constant. Find the work and heat interactions during the expansion process.(10 marks)
**7 (a)** Distinguish between (i) Universal gas constant and particular gas constant (ii) perfect gas ans semiperfect gas.(8 marks)
**7 (b) ** 1 kg of air undergoes a cylic process comparising three process 1-2, 2-3 and 3-1. At state 1 pressure process, 2-3 is reversible adiabatic process ans 3-1 is a reversible isothermal process. At state 3, p=100 kPa.

(i) Sketch the cycle on P-V and T-S coordinates.

(ii) Find the heat and work interaction in each of the three processes and the net work per cycle and

(iii) Analyse quantitatively whether the cycle is reversible or irreversible. (12 marks)
**8 (a)** Explain the following :

(i) Compressibility factor

(ii) Law of corresponding states

(iii) Compressibility chart

(iv) Vander Waals equations of state,(12 marks)
**8 (b)** A mixture of 0.5 kg of carbon dioxide and 0.3 kg of N_{2} is compressed from P_{1}=1 atm, T_{1}=20°C to P_{2}=5 atm in a polytropic process for which n=1.3. Find (i) The final temperature (ii) The work (iii) The heat transfer (iv) The change in entropy of the mixture.(8 marks)