Problems on EntropY
9. A heat engine receives reversibly 420 kl/cycle of heat from a source at 327°C, and
rejects heat reversibly to a sink at 27°C. There are no other heat transfers. For each of
the threehypothetical amounts of heat rejected, in (a). (b), and (e) below and classify
the engine as reversible, irreversible and impossible. (a) 210
kJ/cycle rejected. (b) 105
kJ/cycle rejected and (e) 315 kJ/cycle rejected.
10. Two kg of water at 80°C are mixed
adiabatically with 3 kg of water at 30°C in a
I
constant pressure process of atmosphere. Find the increase in the
entropy of the total
mass of water due to the mixing
process.
11. Air flows through an adiabatic compressor at 2
kg/s. The inlet conditions are I bar
and 310 K and the exit conditions are 7 bar and 560 K. Calculate rate of entropy
generation of universe.
12. A turbine receives a gas (Cp = 1.09 kJ/kg K and Cv = 0.838 kJ/kg K) at 7 bar and
1000°C and discharges at 1.5 bar and 665°C with a heat loss of 10 kJ/kg. Atmosphere
is at 30°C. Determine entropy change of universe.
, 13. One kg of ice at -5°C is exposed to the atmosphere hich is at 20°c. The ice melts
and comes into thermal equilibrium with the atmosphere. A) Determine the entropy
increase of the universe. B) What is the minimum amount of work necessary to
convert the water back into ice at -5° C? Cp of ice is 2.093 kJ/kg K and the latent heat
of fusion is 333.3 kJ/kg.
14. In a closed system air is at a pressure of I bar, temperature of 300 K and volume of
0.025 m. The system executes the following processes during the completion of
thermodynamic cycle: 1-2: constant volume heat addition till pressure reaches 3.8 bar,
2-3: constant pressure cooling of air, 3-1: isothermal heating to initial state. Sketch the
cycle in p-V and T-s plane. Determine the change in entropy in each process. Take Cv
798 J/kg K and R = 287 J/kg K.
15. Prove that increase in entropy in a polytropic process is ds =
ci((7-n)1-n) In(T:/T)
and ds =
e((-n/n) In(p:/pi).
16. In Carnot cycle, the maximum pressure and temperature are limited to 18 bar and
410'C. The volume ratio of isentropic compression is 6 and isothermal expansion is
1.5. Assume the volume of the air at the beginning of isothermal expansion as 0.18
m'. Show the cycle on p-V and T-s diagram and determine i) the pressure and
temperature at main points and i) thermal efficiency of the cycle.
9. A heat engine receives reversibly 420 kl/cycle of heat from a source at 327°C, and
rejects heat reversibly to a sink at 27°C. There are no other heat transfers. For each of
the threehypothetical amounts of heat rejected, in (a). (b), and (e) below and classify
the engine as reversible, irreversible and impossible. (a) 210
kJ/cycle rejected. (b) 105
kJ/cycle rejected and (e) 315 kJ/cycle rejected.
10. Two kg of water at 80°C are mixed
adiabatically with 3 kg of water at 30°C in a
I
constant pressure process of atmosphere. Find the increase in the
entropy of the total
mass of water due to the mixing
process.
11. Air flows through an adiabatic compressor at 2
kg/s. The inlet conditions are I bar
and 310 K and the exit conditions are 7 bar and 560 K. Calculate rate of entropy
generation of universe.
12. A turbine receives a gas (Cp = 1.09 kJ/kg K and Cv = 0.838 kJ/kg K) at 7 bar and
1000°C and discharges at 1.5 bar and 665°C with a heat loss of 10 kJ/kg. Atmosphere
is at 30°C. Determine entropy change of universe.
, 13. One kg of ice at -5°C is exposed to the atmosphere hich is at 20°c. The ice melts
and comes into thermal equilibrium with the atmosphere. A) Determine the entropy
increase of the universe. B) What is the minimum amount of work necessary to
convert the water back into ice at -5° C? Cp of ice is 2.093 kJ/kg K and the latent heat
of fusion is 333.3 kJ/kg.
14. In a closed system air is at a pressure of I bar, temperature of 300 K and volume of
0.025 m. The system executes the following processes during the completion of
thermodynamic cycle: 1-2: constant volume heat addition till pressure reaches 3.8 bar,
2-3: constant pressure cooling of air, 3-1: isothermal heating to initial state. Sketch the
cycle in p-V and T-s plane. Determine the change in entropy in each process. Take Cv
798 J/kg K and R = 287 J/kg K.
15. Prove that increase in entropy in a polytropic process is ds =
ci((7-n)1-n) In(T:/T)
and ds =
e((-n/n) In(p:/pi).
16. In Carnot cycle, the maximum pressure and temperature are limited to 18 bar and
410'C. The volume ratio of isentropic compression is 6 and isothermal expansion is
1.5. Assume the volume of the air at the beginning of isothermal expansion as 0.18
m'. Show the cycle on p-V and T-s diagram and determine i) the pressure and
temperature at main points and i) thermal efficiency of the cycle.
