## Thermodynamics - Jun 2015

### Mechanical Engg (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.

### Answer any one question from Q1 and Q2

**1 (a)** State Kelvin-Planck and Clausius statement of the second law of thermodynamics and prove that the violation of Kelvin-Planck statement results into violation of Clausius statement.(6 marks)
**1 (b)** In a certain heat exchanger, 50 kg of water is heated per minute from 50°C to 110°C by hot gases which enter the heat exchanger at 250°C. If the flow rate of gases is 100 kg/min, estimate the net change of entropy. Assume no loss of heat to surrounding. C_{p(water)=4.186 kJ/kg-K, Cp=1 kJ/kg-K.}(6 marks)
**2 (a)** Derive expression for the following quantities for an ideal gas undergoing a constant temperature process:

(i) Non-Flow System-Work done, Change in internal energy,
Heat transfer

(ii) Flow System Work done, Heat transfer, Entropy change.(6 marks)
**2 (b)** A heat engine working on Carnot cycle absorbs heat from three thermal reservoirs at 1000 K, 800 K and 600 K. The engine does 10 kW of net work and rejects 400 kJ/min. of heat to a heat sink at 300 K. If the heat supplied by the reservoir at 1000 K is 60% of the heat supplied by the reservoir at 600 K, make calculations for the quantity of heat absorbed by each reservoir.(6 marks)

### Answer any one question from Q3 and Q4

**3 (a)** State the assumptions made for air standard cycle. Derive an expression for the air standard efficiency and mean effective pressure of an Otto cycle.(6 marks)
**3 (b)** Steam of mass 10 kg and pressure 1000 kPa, 0.85 dry, is heated at constant pressure till the volume is doubled. Determine:

i) Final quality of steam

(ii) Heat added

(iii) Change in Internal Energy.(6 marks)
**4 (a)** Sketch and explain the construction and working of a separating and throttling calorimeter used for determining the dryness fraction of steam in a boiler.(6 marks)
**4 (b)** A system at 450 K receives 225 kJ/s of heat energy from
a source at 1500 K, and the temperature of both the system
and source remains constant during the heat transfer process. Represent the process on temperature-entropy diagram and determine:

(i) Net change in entropy

(ii) Available energy of heat source and system

(iii) Decrease in available energy.

Take atmospheric temperature equal to 300 K.(6 marks)

### Answer any one question from Q5 and Q6

**5 (a)** Describe briefly the advantages which you would expect to be gained from incorporating an economizer, air preheater, and a superheated in a steam generating plant. By line diagram, indicate the position of these accessories in a typical boiler plant.(6 marks)
**5 (b)** The following data relates to a trial on boiler using economizer, air preheater and superheater:

Condition of steam at exit of boiler = 20 bar, 0.96 dry Temperature of steam at exit of superheater = 300°C

Steam evaporation rate/kg of fuel = 12 kg

Room temperature, t_{0} = 25°C

Temperature of feed water at exit of economizer, t_{1} = 50°C

Temperature of air at exit of air preheater, t_{a} = 70°C

The temperature of flue gases at inlet to superheater, economizer, air preheater and exit of air preheater are respectively 650°C, 430°C, 300°C and 180°C respectively. Assume that air supplied is 19 kg/kg of fuel of calorific value of 45,000 kJ/kg, find:

(i) Equivalent evaporation with and without economizer, from and at 100°C.

(ii) Thermal efficiency of the boiler with and without economizer.

(iii) Thermal efficiency of superheater, economizer and air
Preheater.(7 marks)
**6 (a)** Define steam generator and write down the classification of
Boilers.(6 marks)
**6 (b)** In a certain boiler installation, a steel chimney of 30 m height produces and natural draught equivalent to 17.75 mm of water column. The mean temperature of the boiler house is 298 K and that of hot gases leaving the chimney is 633 K. If the boiler uses 1350 kg of coal per hour, make calculations for:

(i) Air supplied per kg of coal burnt on the grate,

(ii) Draught in terms of column of hot flue gases,

(iii) Density and mass flow rate of hot gas.(7 marks)

### Answer any one question from Q7 and Q8

**7 (a)** Define mass fraction and mole fraction with example and explain the method of writing the complete combustion equation of a C_{8}H_{18} with air.(6 marks)
**7 (b)** A sample of coal supplied to a boiler has the following composition by mass: Carbon = 87%, Hydrogen = 3%, Oxygen = 3%, Nitrogen = 1%, Sulphur = 1% and the remainder is ash. If 15% of excess air is supplied for combustion. Find:

(i) The theoretical amount of air required for complete combustion of fuel

(ii) The mass analysis of flue gas per kg of fuel.(7 marks)
**8 (a)** For what purpose a Bomb calorimeter is used ? Discuss its working with the help of a neat sketch(6 marks)
**8 (b)** The following data pertains to a test run made to determine
the calorific value of a sample of coal:

Mass of coal burnt = 0.85 gm, Mass of fuel wire burnt and its calorific value is 0.028 gm and 6700 kJ/kg respectively, mass of water in calorimeter = 1800 gm, initial and final temperature of water = 16.5°C and 20.25°C, water equivalent of calorimeter = 350 gm, the coal contains 3% moisture by
weight and R.T. = 20°C. Make calculations for the higher and lower calorific values of the coal sample. Consider latent heat of condensation of steam 2460 kJ/kg.(7 marks)