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Basic Thermodynamics Question Paper - Dec 18 - Mechanical Engineering (Semester 3) - Visveswaraya Technological University (VTU)

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## Basic Thermodynamics - Dec 18

### Mechanical Engineering (Semester 3)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Draw neat diagrams wherever necessary.

**Module-1**

**1.a.**Explain Microscopic and Macroscopic approaches to thermodynamics.

**1.b.**State and explain zeroth law of thermodynamic.

**1.c.**The temperature T on a thermometric scale is defined as T = alnK +b were a and b are constants. The values of K are found to be 1.83 and 6.78 at 0$^{\circ} $C and 100$^{\circ}$C respectively. Calculate the temperature for value of K =2.42

**OR**

**2.a.**Obtain an expression for displacement adiabatic work (work done in an adiabatic process).

**2.b.**Define heat and work with reference to thermodynamic point of view.

**2.c.**A gas expands from an initial state where the pressure in 340 KPa and the volume is $0.0425 m^3$ to a final pressure of 136 KPa. The relationship between the pressure and volume of the gas is $PV^2 = constant$. Determine the work done for this process.

**Module-2**

**3.a.**Derive the steady flow energy equation for an open system.

**3.b.**Show that the Kelvin - Planck and Clausiv's statement of the II law of thermodynamic are equivalent.

**3.c.**A gaseous system undergoes three quasistatic processes in sequence. The gas initially at 5 bar $0.01m^3$ is expanded at constant pressure. It is then further expanded according to the relation. $PV^{1.4} = C$ to 2 bar, $0.025m^3$. The gas is then returned to the initial state during which process PV = constant. Calculate the work interaction in each of three process and the net work for the system.

**OR**

**4.a.**Obtain a relation between COP'S of a refrigerator and heat pump.

**4.b.**State and explain the ideal Carnot cycle of P-V diagram.

**4.c.**A series combination of two Carnot engines operates between the temperature of 180$^{\circ}$C and 20$^{\circ}$C. Calculate the intermediate temperature, if the engine produce equal amounts of work.

**Module-3**

**5.a.**Explain the factors that render a process irreversible.

**5.b.**Explain internal and external irreversibility with equation

**5.c.**A reversible engine operates between a source at 927$^{\circ}$C and two sinks at 127$^{\circ}$C and 27$^{\circ}$C. The energy rejected at both the sinks is the same compute the engine efficiency.

**OR**

**6.a.**State and prove Clausius inequality and hence define entropy.

**6.b.**Plot and explain the Carnot cycle with help of temperature entropy diagram.

**6.c.**A 10kg bar of cast iron initially at 400 $^{\circ}$C is quenched in a 20 litres water tank initially at 25$^{\circ}$C. Assuming no heat transfer with the surroundings and no boiling away of liquid water calculate the net entropy change for the process. $Cpcastiron = 0.5$, $Cpwater = 4.187 kJ/kg K$.

**Module-4**

**7.a.**Obtain an expression for maximum useful work for a system and control volume.

**7.b.**Define Gibb's and Helmholtz functions and explain its significances.

**7.c.**Exhaust gases leave an I.C engine at 750$^{\circ}$C and 1 atm, after having done 450kJ per kg gas in the engine cylinder. Assume that the enthalpy of the gas is a function of temperature only and that $C_p = 1.1 kJ/kg K$. Assume the temperature of the surrounding to be 27$^{\circ}$C.

Calculate :

1.The available and unavailable parts of the energy in every kg gas discharged

2.The ratio of available energy to start to the engine work.

**OR**

**8.a.**Sketch and explain Throttling Calorimeter.

**8.b.**Define the following terms :

1.Dryness fraction

2.Latent heat

3.Total heat of wet steam

4.Superheated steam

**8.c.**Find the specific volume, enthalpy and internal energy of wet steam at 18 bar pressure and dryness fraction of 0.85.

**Module-5**

**9.a.**Explain Dalton's law of partial pressure and Amagat's law of additive volumes with reference to ideal gas mixture.

**9.b..**Derive an expression for internal energy and enthalpy of gaseous mixtures.

**9.c.**A mixture of gases contains 1kg of $CO_2$ and 1.5kg of $N_2$. The pressure and temperature of the mixture are 3.5 bar and 27$^{\circ}$C. Determine for the mixture.

1.The mass and mole traction of each constituent gas

2.Average molecular weight

3.The partial pressures.

**OR**

**10.a.**Explain the following :

1.Generalized compressibility chart

2.Law of corresponding states

3.Compressibility factor

**10.b.**Derive Vander Waal's constant interms of critical properties.

**10.c.**Determine the pressure exerted by $CO_2$ in a container of $1.5m^3$ capacities when it contains 5kg at 27$^{\circ}$C.

1.Using ideal gas equations

2.Using Vander Waalâ€™s equation.

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