Basic Thermodynamics - Jan 2012

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) Distinguish between:
(i) Open system and closed system
(ii) Macroscopic ans microscopic approaches
(iii) Point function and path function
(iv) Intensive and extensive properties
(v) Diathermic and adiabatic walls.(10 marks) 1 (b) A thermocouple with test junction and T°cC as a gas thermometer scale ans reference junction at ice point given e.m.f. as e=0.20t -5×10^-4 t² mV. The milli voltmeter is calibrate at ice and steam point. What wiil be e the reading on this thermometer, where the gas thermometer reads 70°C?(10 marks) 2 (a) Distinguish between heat and work in thermodynamics.(4 marks) 2 (b) A system undergoes a process in which the pressure and volume are related by an equation of the from pvⁿ=a constant. Derive an expression for displacement work during this process.(6 marks) 2 (c) A cylinder contains 1 kg of certain fluid ar an initial pressure of 20 bar. The fluid is allowed to expand reversible behind a piston according to a law pv²=c until the volume is doubled, the fluid is then cooled reversibly at constant pressure until the piston regains its original positions, heat is then supply reversibly with the piston firmly locked in position until the pressure rises to the original value. calculate the net work done by the fluid for an initial volume of 0.05m³.(10 marks) 3 (a) Starting from the first law of thermodynamics for a closed system undergoing a non-cuclic process derive the steady state, steady flow energy equation for a control volume (open system).(6 marks) 3 (b) The work and heat transfer per degree termperature change for a systen executes a steady non-flow process are given by $$ \dfrac {dW}{dT}=\dfrac {1}{8}kJ/^{\circ}C \ and \ \dfrac {dQ}{dT}=0.4 kJ/^{\circ}C $$ Determine the change in internal energy of the system, when the temperature increases from 100°C to 260°C.(5 marks) 3 (c) A fluid containedin a cyclinder by a spring loaded frictionless piston so that the pressure in the fluid is the linear function of volume, P=a+bv. The internal energy of the fluid is given by u=34+3.15 PV, where u is in KJ, p is in kPa and v is in m³. If the fluid changes from 170 kPa, 0.03 m³ to a final state of 400 kPa and 0.06m³ with no work other than that done on the piston. FInd the magnitude and direction of heat and work transfers.(9 marks) 4 (a) State and prove that Kelvin Planck and Clausius statements of second law of thermodynamics are equivalent.(10 marks) 4 (b) A reversible engine working in a cycle takes 4800 kg/min of heat from a source at 800 K and develops 20 kW power. The engine rejects heat to two reservoirs at 300 K and 360 K. Determine the heat rejected to each sink.(10 marks) 5 (a) Show that entropy is a property.(5 marks) 5 (b) State and prove Clausius inequality.(8 marks) 5 (c) A heat engine absorbs 200 kJ/sec of heat at 227°C and rejects heat at 27°C. Three separate case of heat rejection are reported.
(i) 180 kj/sec heat is reported
(ii) 120 kJ/sec heat is rejected
(ii) 60 kJ/sec heat is rejected
Classify each cycle.(7 marks) 6 (a) Define the following :
(i) Pure substance
(ii) Triple point
(iii) Critical point
(iv) Quality and
(v) Subcooled liquid(10 marks) 6 (b) A vessel of volume 0.04m³ contains a mixute of saturated water and saturated steam at a temperature of 240°C. The mass of the liquid present is 8 kg. Find the pressure, the mass the specific volume, the enthalpy, the entropy and the internal energy.(10 marks) 7 (a) Show that the change in entropy when a perfect gas undergoes a polytropic change pvⁿ=constant is given by the expression $$ s_2-s_1=\dfrac {\gamma -n}{n-1} \ c,ln\left (\dfrac {T_1}{T_2} \right ) $$(10 marks) 7 (b) One kg of air initially at 1 bar and 160°C is conpressed isothermally till the volume reduces to 0.28 m³. Determine the work done, heat transfer, change in internal energy and the entropy.(10 marks) 8 (a) Obtain expression for the constants 'a', 'b' and 'R' in terms of the critical properties for a vander waal gas.(8 marks) 8 (b) Write a note on compressibility factor and compressibility chart.(6 marks) 8 (c) Determine the pressure exerted by CO₂ in a container of 1.5 m³ capacity when it contains 5 kg at 27°C using (i) Ideal gras equation; (ii) Vander waals equation constants a and b are 365.6k-m²/(kg mol)² and b=0.0428m³/kg-mol, F= universal gas constant=8.3143 kJ/kg mol k.(6 marks)