## Basic 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.
**1 (a)** What do you mean by thermodynamic equilibrium? How does it differ form thermal
equilibrium?(5 marks)
**1 (b)** State zeroth law of thermodynamics. Write its importance in thermodynamics(4 marks)
**1 (c)** Consider a particular Celsius scale assigned the value of 0°C to steam point and 100°C to ice point.

i) Using ideal gas as the thermometer medium, setup relationship between 0°C and pressure for a constant volume thermometer, proceed to derive the correction between the two Celsius scales. At what temperature are two scales are numerically equal?

ii) What is the numerical value of absolute zero particular scale? What is 200 K
in °C?(7 marks)
**1 (d)** Two Celsius thermometers A and B with temperature readings T_{A} and T_{B} agree at ice point and steam point, but else where they are related by T_{A} = p + qT_{ B} + rT^{2}_{B} , where p, q and r are constants. When the thermometers are immersed in an oil bath, A shows a temperature of 51°C while B shows 50°C. Determine the temperature T_{A} when T is 25°C(4 marks)
**2 (a)** Define work and heat. Write the similarities and dissimilarities between them(6 marks)
**2 (b)** An automobile vehicle of 1500 kg is running at a speed of 60 km/hr. The brakes are
suddenly applied and the vehicle is brought to rest. Calculate the rise in temperature of brake shoes, if their mass is Take the specific heat of brake shoe material as 0.46 KJ/kgK.(6 marks)
**2 (c)** A quantity of gas compressed in a piston-cylinder from a volume of 0.8611 m^{3} to a final volume of 0.17212 m^{3}. The pressure (in bar) as a function of volume (m^{3}) is given by,

i) $$p=\frac{0.86110}{V}-\frac{8.60673\ ×10^{-5}}{V^{2}}$$

i) Find the amount of work done in KJ

If the atmospheric pressure, i.e. 1 bar acting on the other side of piston is considered find the net work done in KJ(6 marks)
**2 (d)** State direction of heat transfer and work transfer in a viscous fluid is stirred by a paddle wheel in an insulated closed tank(2 marks)
**3 (a)** What is a perpetual motion machine of first kind> why is it impossible ?(3 marks)
**3 (b)** Apply steady flow energy equation to each of the following

i) Boiler ii) Nozzle iii) Centrifugal pump(6 marks)
**3 (c)** 1200 kg car cruising steadily on a level road at 90 km/hr. Now the car starts climbing a hill that is sloped 30° from the horizontal. If the velocity of the car is to remain constant during climbing, determine the additional power that must be delivered by the engine(4 marks)
**3 (d)** A centrifugal pump delivers 50 kg of water per second. The inlet and outlet pressure are
1 bar and 4.2 bar respectively. The suction is 2.2 m below the centre of the pump and
delivery is 8.5 m above the centre of the pump. The suction and delivery pipe diameters are 200 mm and 100 mm, respectively. Determine the capacity of electric motor to run the pump.(7 marks)
**4 (a)** Prove that a reversible engine is more efficient than an irreversible engine operating between the same temperature limits(6 marks)
**4 (b)** A house hold refrigerator maintains a Space at a temperature of 0°C. Every time the door is opened, warm material is placed inside, introducing an average 400 KJ of heat. but making only a small change in temperature of the refrigerator. The door is opened 25 times a day and the refrigerator operates at 25% and ideal COP. The cost of work is 3.50 per kWh. What is the monthly bill of this refrigerator? The atmospheric temperature is at 30°C.(6 marks)
**4 (c)** Explain the second law of thermodynamics with reference to Kelvin Planck's statement and Clausius statement hence prove that both the statements are equivalent to each other although they appear to be different(8 marks)
**5 (a)** Prove that for a system executing a cyclic process $$\oint \frac{\delta Q}{T}\leq 0$$ hence define entropy(8 marks)
**5 (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.

C_{p}(water)=4.186 KJ/kgK, C^{p(gas)=1KJ/kgK.}(6 marks)
**5 (c)** A piston-cylinder arrangement contains 0.03 m^{3} of nitrogen at 1 bar and 290 K. The piston moves inwards and the gas is compressed isothermally and reversibly until the pressure becomes 4 bar. Determine change in entropy work done. Assume nitrogen to be a perfect gas.(6 marks)
**6 (a)** Define the following

i)Triple point

ii) Critical temperature

iii) Dryness fraction

iv) Saturation temperature(4 marks)
**6 (b)** Sketch and explain the construction and working of a separating and throttling calorimeter used for determining the dryness fraction of steam in a boiler(8 marks)
**6 (c)** Identify the type of steam in the following theree cases, using the steam tables and giving necessary calculations supporting your claim

i) 2kg of steam at 8bar with an enthalpy of 5538.0 KJ at a temperature of 170.4°C

ii) 1 kg of steam at 2550 kPa occupies a volume of 0.2742 m^{3}. Also find the stream temperature.

iii) 1 kg and steam at 60bar with an enthalpy of 2470.73 kj/Kg(8 marks)
**7 (a)** Write notes on the following i)Clausis-Clapeyron equation

ii) Maxwell's equation(8 marks)
**7 (b)** Derive an expression for change in entropy for an ideal gas undergoing

i) an isobaric process and

ii) a polytropic process(6 marks)
**7 (c)** One kg of air undergoes a cycle composed of the following three reversible processes.

i) Constant pressure expansion from 0.1 MPa and 300K to 400K.

ii) An isothermal compression to restore the gas to 0.1MPa

sketch the P-V diagram for the above cycle and estimate the entropy changes for the three processes(6 marks)
**8 (a)** Write notes on the following i) Compressibility factor ii) Compressibility chart iii) Law of corresponding states(9 marks)
**8 (b)** A volumetric analysis of a gaseous mixture yields the following result

CO_{2}=12%, O_{2}=4%, N_{2}=82%, CO=2%

Determine the analysis on a mass basis and the molecular wight and the gas constant on a mass basis for the mixture. Assume ideal gas behaviour(8 marks)
**8 (c)** Define the terms partial pressure mole fraction, volume fraction of a gas constituent in a mixture(3 marks)