## Basic Thermodynamics - Dec 2015

### 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)** Differentiate between: (i) Control mass and control volume (ii) Intensive and extensive properties, and classify the following into intensive and extensive properties, (i) Enthalpy (ii) Quality of steam (iii) Entropy and (iv) Density.(6 marks)
**1 (b)** Define the zeroth law of thermodynamics and explain how this law forms the basis for temperature measurement.(6 marks)
**1 (c)** A constant volume gas thermometer containing helium gas gives readings of gas pressure 1000 mm and 1366 mm of mercury at the ice point and steam point and steam point respectively.

i) Express the gas thermometer Celsius temperature in terms of gas pressure

ii) The thermometer when left standing in the atmosphere, registers 1075 mm of mercury. Determine the atmospheric temperature.(8 marks)
**2 (a)** Write the thermodynamic definition of work. With suitable example explain how it is more general than the definition of work in mechanics.(4 marks)
**2 (b)** A gas expands quasi-statically in a piston cylinder arrangement against the atmosphere and a spring Initial pressure and volume are 400 KPa and 0.2 m^{3} respectively. The final volume of gas is 0.6 m^{3}. Determine the total work done by the gas if the spring force is proportional to volume of the gas. Assume the atmospheric pressure as 101.325 KPa.(8 marks)
**2 (c)** A spherical balloon of 1m diameter contains a gas at 200 KPa. The gas inside the balloon is heated until the pressure reaches 500 KPa. During the process of heating, the pressure of the gas inside the balloon is proportional to the diameter of the balloon. Calculate the work done by the gas inside the balloon.(8 marks)
**3 (a)** Write the first law equation for a closed system undergoing a non cyclic process and show that internal energy is a property of a system.(8 marks)
**3 (b)** Modify the general steady flow energy equation (SFEE) for the following cases:

i) Steam turbine with negligible potential energy change if the process is adiabatic.

ii) Horizontal steam nozzle with negligible entrance velocity of steam, if the process is non-adiabatic.

iii) Insulated horizontal throttle valve.(6 marks)
**3 (c)** In a centrifugal compressor, the suction and delivery pressure are 100 Kpa and 550 Kpa respectively. The compressor draws 15 m^{3}/min of air which has a specific volume of 0.77 m^{3}/kg. At the delivery the specific volume is 0.20 m^{3}/ kg. The compressor is driven by a 40 KW motor, and heat lost to the surroundings during compression is 30 KJ/kg of air. Neglecting change in potential and kinetic energy, calculate increase in internal energy per kg of air.(6 marks)
**4 (a)** Write Kelvin-Planck and Clausius statements of second law of thermodynamics. Show that violation of Clausius statement leads to the possibility of a perpetual motion machine of second type.(10 marks)
**4 (b)** Mention the factors that make a process irreversible.(4 marks)
**4 (c)** Using a heat engine of thermal efficiency 30% to drive a refrigerator having a COP of 5, what is the heat received by the heat engine for each MJ of heat removed from the cold body of the refrigerator.(6 marks)
**5 (a)** Derive Clausius inequality and prove that entropy is a property.(10 marks)
**5 (b)** Explain the principle of increase of entropy.(4 marks)
**5 (c)** Two copper blocks weighing 10 kg each are initially at temperature of 227°C and 27°C respectively. What is the change in entropy when these two blocks are brought into contact with each other? Take specific heat of copper as 0.4 Kj/kgK.(6 marks)
**6 (a)** Define the following: (i) Pure substance ii) Triple point

iii) Critical point.(6 marks)
**6 (b)** With neat sketch explain the measurement of dryness fraction of steam by using throttling calorimeter.(8 marks)
**6 (c)** Calculate the internal energy per kg of superheated steam at pressure of 10 bar and a temperature of 300°C. Also find the change in internal energy if this steam is expanded to 1.4 bar and dryness fraction 0.8.(6 marks)
**7 (a)** Starting from the relation Tds=du+Pdv, show that for an ideal gas undergoing a reversible adiabatic process, the law for the process is given by TV^{y-1} = Constant.(6 marks)
**7 (b)** Clearly distinguish between ideal and real gases.(4 marks)
**7 (c)** A quantity of air at a pressure of 100 KPa. 27°C occupying a volume of 0.5 m^{3} is compressed to a pressure of 500 KPa and volume of 0.12 m^{3} according to the law PV^{m}=constant. Find (i) The value of index 'n' (ii) The mass of air (iii) Work transfer (iv) Heat transfer during the process (v) Change in entropy.(10 marks)
**8 (a)** Write the Vander equation of state. In what says, it is an improvement over the ideal gas equation.(6 marks)
**8 (b)** Explain the following:

i) Compressibility factor

ii) Reduced properties

iii) Law of corresponding states

iv) Generalised compressibility chart.(8 marks)
**8 (c)** Determine the specific volume of hydrogen gas when its pressure is 60 bar and temperature is 100 K by using (i) Compressibility chart (ii) Vander Waal's equation Take for H_{2} T_{C}=239.76°C, P_{C}=12.92 bar, a=0.25105 × 10^{5} Nm^{2}/kgmol^{4}, b=0.0262 m^{3}/kgmole.(6 marks)