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## Applied Thermodynamics - Dec 2013

### Mechanical Engg (Semester 4)

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.

### Answer any one question from Q1 and Q2

**1 (a)** State and prove the equivalency of Kelvin Planck and Clausius statement.(6 marks)
**1 (b)** Prove: S_{2}-S_{1}=C_{v}lm(T_{2}/T_{1})+R ln(V_{2}/V_{1}).(6 marks)
**1 (c)** State the limitations of First law of thermodynamics. How does the second law of thermodynamic overcome these limitations.(4 marks)
**10 (a)** Discuss the factors those influence the volumetric efficiency of a reciprocating air compressor.(6 marks)
**10 (b)** A two stage single acting reciprocating compressor takes in air at the rate of 0.2 m^{3}/s. The intake pressure and temperature of air are at 0.1 Mpa and 16°C. The air compressed to a final pressure of 0.7 Mpa. The intermediate pressure is ideal and inter-cooling is perfect. The compression index in both the stages is 1.25 and the compressor runs at 600 RPM. Neglecting clearance, determine:

i) The intermediate pressure

ii) The total volume of each cylinder

iii) The power required to drive the compressor

iv) The rate of heat rejection in the intercooler.

Take:

C_{p}=1.005 kJ/kgK and R=0.287 kJ/kgK.(10 marks)

### Answer any one question from Q11 and Q12

**11 (a)** Differentiate between mountings and accessories of the boiler. Give at least two examples of each.(8 marks)
**11 (b)** In a boiler test 1250 kg of coal are consumed in 24 hours. The mass of water evaporated is 13000 kg and mean effective pressure is 7 bar. The feed water temperature was 40°C, heating value of coal is 30000 kJ/kg. The enthalpy of 1 kg of steam at 7 bar is 2570 kJ. Determine:

i) Equivalent evaporation per kg of coal

ii) Efficiency of the boiler.(10 marks)
**12 (a)** Explain the following terms:

i) Boiler efficiency

ii) Equivalent evaporation.(8 marks)
**12 (b)** A boiler produces 200 kg of dry saturated steam per hour at 10 bar and feed water is heated by an economizer to a temperature of 100°C. 225 kg of coal of a calorific value 30100 kJ/kg are fired per hour. If 10% of coal remains unburnt, find the thermal efficiency of the boiler and the boiler grate combined.(10 marks)
**2 (a)** State and prove the Clausius Inequality.(8 marks)
**2 (b)** 5 kg of air is expanded at a constant pressure to four times its initial volume. The initial temperature of air is 400°C. It is then brought to its original temp, by a constant volume change. Calculate the entropy change.(8 marks)

### Answer any one question from Q3 and Q4

**3 (a)** Explain the following:

i) Available and unavailable energy

ii) Principal reasons for irreversibility

iii) Helmholtz and Gibbs function.(9 marks)
**3 (b)** Calculate the decrease in available energy when 20kg of water at 90°C mixes with 30 kg of water at 30°C, the pressure being taken as constant and the temperature of surrounding is 10°C (C_{p} for water 4.18 kJ/kgK).(7 marks)
**4 (a)** Derive an expression for work transfer in reversible adiabatic process.(7 marks)
**4 (b)** 1 kg of air at pressure of 8 bars and temp. of 100°C undergoes a reversible polytropic process following the law pv^{1.2}=C. If the final pressure is 1.8 bars, determine:

i) Final specific volume, temperature and increase of entropy.

ii) The work done and heat transfer.

Assume R=0.287 kJ/kgK.(9 marks)

### Answer any one question from Q5 and Q6

**5 (a)** With the help of T-S diagram, explain the effect of the following parameters on the performance of Rankine cycle:

i) Effect of superheat

ii) Condenser pressure.(8 marks)
**5 (b)** A steam turbine receives superheated steam at a pressure of 17 bar and having degree of superheat of 110°C. The exhaust pressure is 0.07 bar and expansion of steam takes place isentropically.

Calculate:

i) The heat supplied and heat rejected

ii) Network output

iii) Thermal efficiency

iv) Specific steam consumption.

Neglect pump work.(10 marks)
**6 (a)** Explain the following terms:

i) Critical point

ii) Dryness fraction.(4 marks)
**6 (b)** With the help of a neat sketch explain the working of separating and throttling calorimeter.(6 marks)
**6 (c)** Steam at 7 bar and 250°C has a volume of 0.5046 m^{3}. In a frictionless constant volume process the pressure changes to 3.5 bars. Find the final temperature and heat transfer. Also determine the change in entropy.(8 marks)

### Answer any one question from Q7 and Q8

**7 (a)** Write a short note on calorific value of a fuel.(5 marks)
**7 (b)** A coal sample gave the following analysis by weight, Carbon 85%, Hydrogen 6%, Oxygen 6%, the remainder being incombustible. Determine minimum weight of air required per kg of coal for chemically correct composition.(6 marks)
**7 (c)** Explain NDIR method of gas analysis in brief.(5 marks)
**8 (a)** Write a note on theoretical and excess air.(5 marks)
**8 (b)** The following particulars refer to an experimental determination of the calorific value of a sample of coal containing 88% C and 4.2% H_{2}. Weight of coal =0.848 gm, weight of fuse wire 0.027 gm, of calorific value 6700 J/gm, weight of water in the calorimeter=1950 gm, water equivalent of calorimeter=380 gm, observed temperature rise=3.06°C, cooling correction = +0.017°C. Find the higher and lower calorific values of the coal.(6 marks)
**8 (c)** With the help of neat sketch discuss the method of determining calorific value of gaseous fuel.(5 marks)

### Answer any one question from Q9 and Q10

**9 (a)** What are the advantages and disadvantages of multistage reciprocating air compressor?(6 marks)
**9 (b)** A single stage reciprocating compressor takes 1 m^{3} of air per minute at 1.013 bar and 157deg;C and delivers it at 7 bar. Assuming that the law of compression is pV^{1.35}=constant, and the clearance is negligible, calculate the indicate power.(10 marks)