## Basic Thermodynamics - Jun 2014

### 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

i) Open system ii) Closed system and iii) Isolated system and classify the following into closed and isolated and explain giving reasons:

i) Radiator of a car ii) Thermos flask iii) Water pump & iv) Pressure cooker.(7 marks)
**1 (b)** What are international fixed reference points? Name few of them. What is their importance?(5 marks)
**1 (c)** Define a new temperature scale'N' in which freezing point and boiling point of water are 100°N and 300°N respectively. Correlate this temperature scale with centigrade scale for which freezing and boiling are 0° C and 100°C respectively.(8 marks)
**2 (a)** Starting from a convenient common state point, on P-V diagram, show the four expansion processes called? Indicate their names adjacent to the processes on the diagram.(6 marks)
**2 (b)** Show that work and heat are path functions.(4 marks)
**2 (c)** To a closed system 150 kJ of work is done on it. If the initial volume is 0.6m^{3} and pressure of system varies as follows.

P=(8-4V),

Where 'P' is pressure in bar and 'V' is volume in m^{3}. Determine the final volume and pressure of the system.(10 marks)
**3 (a)** Write the steady flow energy equation for an open system and explain the terms involved in it, and simplify SFEE for the following systems:

i) Steam turbine ii) Nozzle.(6 marks)
**3 (b)** The properties of a certain fluid are related as follows:

u=0.718t+196

Pv=0.287(t+273).

where 'u' is specific internal energy(kJ/kg), 't' is temp in °C, 'P' is pressure in (kN/m^{2}) and 'v' is specific volume in(m^{3}/kg). For this fluid find c<sub<p< sub=""> and cv(ie. Specific heat and constant pressure and specific heat at constant volume). If a system composed of 2 kg of this fluid expands in a frictionless piston and cylinder machine from an initial state of 1 MPa, 100°C to a final temperature of 30°C. If there is no heat transfer, find the net work for the process.</sub<p<><>(8 marks)
**3 (c)** A blower handles 1 kg/s of air at temperature of 20°C and consumes a power of 15kW. The inlet and outlet velocities of air are 100m/sec and 150m/sec respectively. Find the exit temperature of air, assuming adiabatic conditions. Take c_{p}=1.005 kJ/kg K.(6 marks)
**4 (a)** State and prove Comot's theorem.(10 marks)
**4 (b)** A heat engine is used to drive a heat pump. The heat transfer from the engine and heat pump are used to heat water circulating throught the radiators of a buildings. The efficiency of the heat engine is 27 percent and coefficient of performance of heat pump is 4. Evaluate tha ratio of the heat transfer to the radiator circulating water to the heat transfer to the engine.(10 marks)
**5 (a)** State and prove Clausius inequality? What is the significance of Clausius inequality>(10 marks)
**5 (b)** An diabatic vessel contains 85 kg of oil at a temperature of 27°C. A spherical ball made of steel of 10 kg at 727°C is immersed in oil. Determine change in entropy for the universe. Take specific heat of oil=3.5 kJ/kg K; specific heat of steel ball=0.5 kJ/kg K.(10 marks)
**6 (a)** Define dryness fraction of steam? What are methods used to measure dryness fraction> with neat sketch explain any one method.(10 marks)
**6 (b)** A rigid vessel of 2 m^{3} volumes is filled with superhead steam at 20 Bar and 350° C. The vessel is cooled until the steam is just dry saturated. Calculate the mass of steam in the vessel; the final pressure of steam and amount of energy transferred as heat to the surroundings.(10 marks)
**7 (a)** Write Maxwell relations and explain the terms involved(4 marks)
**7 (b)** Show that the change in entropy when a perfect gas undergoes a polytropic change PV^{n=Constant is given by the expression(s_{2}-s_{1})=c_{v}\left ( \frac{r-n}{n} \right )n\left ( \frac{P_{1}}{P_{2}} \right )}(6 marks)
**7 (c)** 0.2 kg of air with pressure 1.5 bar and temperature 87°C is compressed to a pressure of 15 bar according to the law PV^{1.25}=constant. Determine i) work done on or by the air. ii) Heat flow to or from the air iii) Change of entropy stating whether it is an increase or decrease in entropy. For air R=0.287 kJ/kg K, r=1.4, C_{v}=0.718 kJ/kg K(10 marks)
**8 (a)** Write notes on the following

i) Dalton's law of partial pressures

ii)Vander Waal's equation of state

iii) Generalized compressibility chart(12 marks)
**8 (b)** Determine the pressure exerted by carbon dioxide in a container of 1.5m^{3} capacity when it contains 5 kg at 27 ° C by using

i0 Ideal gas equation ii) Van Der Waal's equation

Take the Van Der Waal's constant a=365.6 kN-m^{4}/(kgmol)^{2}; b=0.0428 m^{3}/kgmol

Universal gas const=\bar{R}=8.3144 kJ/kgmol K.(8 marks)