ME2100 Applied Thermal Engineering
Tutorial 1 - Entropy
1. An insulated box is divided into two compartments A and B by a negligibly thin
partition. Compartment A initially contains 10 kg of N 2 (MW = 28 kg/kmol, = 1.4)
at 500 K and 500 kPa and compartment B initially contains 2 kg of H 2 (MW = 2
kg/kmol, = 1.4) at 300 K and 100 kPa. The partition is now removed and the
gases are allowed to mix and reach an equilibrium state. Taking the box as the
system, determine its entropy change. [8.3855 kJ/K]
2. Two kg of ice at -15 oC is dropped into 10 kg of liquid water initially at 27 oC in an
insulated container. Simultaneously, 3500 kJ of work is transferred to the container
by means of a paddle wheel. Determine (a) the final temperature and (b) entropy
change. The latent heat of melting of ice is 334 kJ/kg, specific heat capacity of ice
is 2.03 kJ/kg.K and that of water is 4.2 kJ/kg.K. [(a) 77.48oC, (b) 11.3068 kJ/K]
3. A steel casting (specific heat 500 J/kg.K) of mass 20 kg initially at 200 oC is to be
cooled to room temperature (27oC). It is first kept in a furnace that is maintained at
140oC and then moved to a water bath that is initially at room temperature. It is
finally allowed to cool in the ambient air. Determine the entropy generated during
this process. The water bath may be assumed to contain 80 kg of water (specific
heat capacity 4200 J/kg.K) and heat loss from the bath to the ambient may be
neglected. [0.6396 kJ/K]
4. Five kg of saturated R134a vapor at -15 oC is contained in a rigid vessel. The R134a
is stirred by transferring an amount of work equal to 500 kJ. Simultaneously, heat
transfer to the ambient at 30oC also takes place until the content of the vessel
reaches the ambient temperature. Determine the entropy generated during the
process. [1.7 kJ/K]
5. Steam steadily enters an insulated turbine at 10 kg/s, 60 bar, 400 oC and exits at 10
bar, 190oC. Determine the power developed and rate of entropy generation.
Neglect KE and PE changes. [3731.5 kW, 0.992 kW/K]
6. R134a steadily enters an adiabatic compressor with a mass flow rate of 0.5 kg/min,
as saturated vapor at -5oC and leaves at 700 kPa, 40oC. Neglect KE and PE
changes. Determine the compressor power and the rate of entropy generation.
[15.525 kJ/min, 0.01485 kJ/K.min]
7. Steam at 10 bar, 420 oC steadily enters an adiabatic nozzle with negligible velocity. It
is expanded in the nozzle to 1 bar, 160 oC. Neglecting PE changes, determine the
exit velocity and rate of entropy generation. [1010 m/s, 0.1318 kW/K]
8. Water at 200 kPa and 30oC enters the mixing chamber of a waste heat recovery unit
at a rate of 5 kg/s where it is mixed with steam at 200 kPa and 200 oC. Heat loss to
the surrounding air at 27 oC occurs at a rate of 10 kW. If the mixture is required to
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leave at 200 kPa and 80oC, determine the required mass flow rate of steam and
the rate of entropy generation. [0.4166 kg/s, 537.5 W/K]
9. Air is contained in a rigid tank of volume 1000 L. The air is initially at 1 MPa, 300 K.
A valve on the top of the tank is now opened and the air is allowed to escape
slowly into the atmosphere until the pressure in the vessel reaches 100 kPa at
which point, the valve is closed. Temperature of air inside the tank is maintained
constant as a result of heat transfer with the ambient at 27 oC. Determine the mass
of air that escapes, heat transfer and the entropy generated during the process.
KE and PE changes are neglected. [10.45 kg, 900 kJ, 0 kJ/K]
10. A rigid vessel initially contains 1 kg of saturated R134a vapor and 15 kg of saturated
R134a liquid at 900 kPa. A relief valve is provided on the top of the vessel to
maintain the pressure inside the vessel constant at 900 kPa by allowing saturated
vapor to escape. Heat is added from a reservoir at 50 oC to the vessel until all the
liquid evaporates. Find the mass of vapor that escapes, heat supplied and entropy
generated. [14.43 kg, 2515.185 kJ, 361.54 J/K]
11. A rigid vessel of volume 600 L contains 8 kg of water at 20 bar. Liquid is now
allowed to escape slowly from the bottom of the vessel. Heat is transferred from a
reservoir at 250oC to the vessel so as to maintain the pressure constant. The
process is stopped when no more liquid remains in the vessel. Find the mass that
escapes, heat transferred and entropy generated. [1.976 kg, 45.22 kJ, 6.362 J/K]
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