Jadavpur University 2007 B.E Mechanical Engineering THERMODYNAKICS-I - Question Paper

EX/ME/T/126/76/2006
FIRST B. E. MECHANICAL ENGG. EXAMINATION, 2006
(2nd Semester)
THERMODYNAMICS -I
Time:Three hours Full Marks : 100
ans any 5 (5) ques..
All ques. carry equal marks.
Use of Steam tables is permitted.
If any data is not available, the identical may be presumed
consistently with the issue.
1 (a) describe critical point and triple point for a pure
substance. 4
(b) A vessel having a quantity of 0.4m3 contains 2.0 kg of
a liquid water and water vapor mixture in equilibrium
at a pressure of 600 kPa. compute the quantity and
mass of vapor 8
(c) A rigid vessel having a quantity of 15 Litres contains
10 kg of water (liquid + vapor) at 30°C. The vessel is
now slowly heated. Will the liquid level inside eventually
rise to the top or drop to the bottom of the
vessel? What if the vessel contains one kg instead of
10 kg? 8
2. (a) Show the similarities and differences, if any ranging from
heat and work. 4
(b) Air is contained in a piston cylinder arrangement. The
initial quantity inside the cylinder is 100 Litres, at which
state the pressure inside is 100 kPa. The spring is touching
the piston at this state but exerts no force on it.
[Turn over]
( two )
Heat is now transferred to the system, causing it to
expand until the quantity is doubled, at which state the
pressure in the cylinder is 300 kPa. During the process
the spring force is proportional to the displacement
of the piston from its initial position.
(i) Show the process on a P-V diagram.
(ii) Considering the air inside the cylinder as the system,
compute the work done by the system.
What percentage of this work is done against the
spring? 14
(c) discuss the concept of continuum? 2
3 (a) Starting from the formula of the 1st legal regulations of
Thermodynamics for a control volume, develop the
equations for a steady state steady flow (SSSF)
process and also for an uniform state uniform flow
(USUF) process. 10
(b) Super heated vapour steam enters a turbine nozzle at
3 MPa, 350°C with a low velocity and exits the nozzle
at 1.6 MPa with a velocity of 550 m/s. The steam mass
flow rate is 0.5 kg./s. compute the quality of steam if
it is wet saturated at nozzle exit or the temperature of
the steam exiting the nozzle if it is super heated. Also
obtain the exit area of the nozzle. 10
4. (a) Show that the Kelvin-Planck and Clausius statements
of the 2nd legal regulations of Thermodynamics are equivalent.
Also prove that all engines operating in the Carnot
cycle ranging from 2 provided constant temperature
reservoirs have the identical efficiency. 10
( three )
(b) 2 reversible heat engines A and B are organizes in
series. Engine A receives 200KJ at a temperature of
421°C from a high temperature thermal source and is
rejecting heat directly to a different thermal reservoir from
which the engine B. receives heat and reject to a cold
sink at temperature 4.4°C. If the work output of
engine A is twice that of engine B, obtain (a) the
temperature of the thermal reservoir ranging from A and B
(b) the efficiency of every engine, and (c) the heat
rejected to the cold sink. 10
5 (a) Prove that the change of entropy for any process can
be expressed as an equality of the form,
where terms have their usual
meanings. 10
(b) Consider the reversible adiabatic flow of steam through
a nozzle. Steam enters the nozzle at one MPa, 300°C.
with a velocity of 30 m/s. The pressure of the steam
at the nozzle exit is 0.3 MPa. Determine the exit
velocity of the steam from the nozzle, assuming a
reversible, adiabatic, steady-state, steady-flow process.
10
6 (a) Prove the Clapeyron formula
where the terms as their usual meanings. 12
(b) Prove that for closed system ds system + ds surrounding = 0 4
[Turn over]
( four )
(c) Show that in the Temperature-Entropy plane the
constant quantity process line has a greater slope than
the constant pressure process. 4
7 Write short notes on any 4 of the subsequent : 5×4 = 20
(a) Clausius inequality
(b) Generalised Compressibility Chart
(c) Availability of a system
(d) Proof of Maxwell relation (?v / ?T)P = –( ?s / ?P)T
(e) 1st legal regulations of thermodynamics as a rate formula
(f) Assumptions of SSSF and USUF processes.
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Earning:   Approval pending.