CEBU INSTITUTE OF TECHNOLOGY – UNIVERSITY
N. Bacalso Avenue, Cebu City, Philippines
COLLEGE OF ENGINEERING AND ARCHITECTURE
Department: MECHANICAL ENGINEERING
METE 231 – THERMODYNAMICS
PROBLEM SET
NAME OF STUDENT:_____________________ ID #__________Section:____Date:___________
Instruction:Solve the following problems with complete solutions using your ID# as
illustrated above. Make sure your solutions are written neatly. Box your final
answer.
1. A Carnot heat engine operates between two thermal reservoirs. It receives 1200
kJ of heat and produces 450 kJ of net work.
a. Determine the ratio of the temperature.
b. If the high-temperature reservoir is fixed at TH = 900K, find TL.
c. If the engine is redesigned to increase work output to 600kJ per cycle,
explain using Carnot principles why this is imposible without changing
the reservoir temperatures.
2. A proposed engine receives 500 kJ of heat from a single reservoir at 550 K
and produces 150 kJ of net work, rejecting the remaining energy into the same
reservoir.
a. Identify the specific statement of the second law violated.
b. Using Lecture 6 discussion, classify this device as a PMM1 or PMM2 and
justify.
3. A refrigerator removes QL = 2.2 kW from a cold space at 0°C while rejecting
heat to a room at 30°C. The refrigerator has an actual COP that is 40% of the
COP
of
a
reversible
(Carnot)
refrigerator
operating
between
the
same
temperatures.
a. Determine the actual work input.
b. If an additional 0.3 kW of heat leaks into the refrigerated space due
to poor insulation, calculate the new work input required.
4. Consider two compression processes of an ideal gas from the same initial to
final states:

Process A: Quasi-equilibrium, internally reversible compression

Process B: Fast compression with significant pressure gradients
Using Chapter 6 descriptions,
a. Discuss qualitatively which process requires more work input and why.
b. Identify the type(s) of irreversibility present.
c. Explain why reducing the compression speed makes the process approach
reversibility.
5. A reversible heat engine operates between two reservoirs at temperatures TH
and T. It receives 800kJ of heat from the high-temperature reservoir and
rejects 300kJ to the reservoir at temperature T.
a. Using the thermodynamic temperature scale, compute the T/TH.
b. If the low-temperature reservoir is known to be at 350K, Determine TH.
6. A Carnot heat pump maintains a house at 20°C while the outdoor temperature is
–5°C. The pump must supply 45,000 kJ/h to the house.
a. Compute the minimum (reversible) work input.
b. An actual heat pump requires 3 times the theoretical minimum work.
Determine its actual COP.
c. Compare the result to the Carnot COP and explain the cause using
irreversibility concepts.
7. A researcher claims to have built a heat pump that keeps a cold room at 0°C
while heating a nearby water tank to 55°C, without consuming any power, by
“recycling heat internally.”
a. Identify the violated second-law statement.
b. Explain whether this is a PMM1 or PMM2.
c. Explain why such a device cannot exist even if perfect insulation is
assumed.
8. A working fluid in a Carnot heat engine undergoes four reversible processes
in a P-V Diagram. Given initial state: P1=300 Kpa, V1=0.04m3, TH=500K and after
isothermal expansion, volume doubles.
a. Determine the heat input.
b. Compute total net work using Carnot efficiency.
c. Explain physically why isothermal heat addition must occur at the maximum
temperature.
9. A household refrigerator rejects 900 kJ/h to the kitchen at 27°C. The
evaporator absorbs QL = 550 kJ/h.
a. Compute the COP of the refrigerator.
b. Compare this to the COP of a reversible refrigerator operating between
the same temperatures.
c. Explain why actual refrigerators are far from reversible, citing at least
two irreversibilities.
10.
Two heat engines operate between the same reservoirs at TH = 800 K and
TL = 300 K.

Engine A produces 120 kJ of work per cycle from 400 kJ of heat input.

Engine B claims to produce 180 kJ of work from the same heat input.
a. Determine whether Engine A conforms to the second law.
b. Determine whether Engine B is possible.
c. Using Carnot’s second principle, prove why Engine B is impossible
independent of working fluid or cycle details.
11.
A steam power plant operates on a simple Rankine cycle with boiler
pressure of 8 MPa and condenser pressure of 10 kPa. A Carnot vapor cycle
operates between the same maximum and minimum temperatures as the real Rankine
cycle.
a. Estimate the maximum possible thermal efficiency (Carnot efficiency) of
any cycle operating between these temperatures.
b.
Explain why a Carnot vapor cycle cannot be practically implemented using
water/steam, citing at least three technical limitations.
c.
Discuss qualitatively how irreversibilities in the pump, boiler, and
turbine create a gap between actual Rankine efficiency and the Carnot
limit.
12.
A Carnot vapor cycle uses water as the working fluid. The turbine inlet
temperature is 450°C, and the condenser operates at 40°C. It is required that
the turbine exit vapor quality be at least 90%.
a.
Determine whether this Carnot cycle can operate without violating the
quality constraint.
b.
Explain why the isentropic expansion in a Carnot vapor cycle leads to
very low quality at the turbine exit.
c.
Based on your answer, justify why steam power plants use Rankine cycles
instead of Carnot cycles.
13.
A Rankine cycle receives heat at constant pressure in the boiler at 3
MPa, and rejects heat at 20 kPa. The Carnot cycle, however, requires isothermal
heat addition and rejection.
a.
Using the concept of reversible processes, explain why pump work in the
Rankine cycle is not negligible compared to that of a Carnot vapor cycle.
b.
Derive how the presence of liquid water in the pump stage leads to
significantly lower pump work than turbine work.
c.
Discuss how neglecting pump work affects the difference between Carnot
and Rankine efficiency predictions.
14.
A power plant engineer compares the back-work ratio (BWR) of a simple
Rankine cycle with a hypothetical Carnot vapor cycle operating between the
same temperature limits.
a.
Define back-work ratio for vapor cycles.
b.
Explain qualitatively which cycle (Carnot or Rankine) has the higher
BWR, and why.
c.
Discuss
how
turbine
outlet
quality
and
compressor/pump
irreversibilities influence the BWR in real Rankine plants.
15.
A
Rankine
steam
power
plant
receives
heat
at
500°C
from
a
high-
temperature source and rejects heat to a condenser at 30°C. The boiler supplies
steam at a rate of 1.8 kg/s, and the enthalpy rise in the boiler is 2900
kJ/kg. Assume Carnot efficiency gives the upper limit of power production.
a.
Compute the Carnot efficiency based on the temperature limits.
b.
Determine the maximum theoretical power output of the plant (Carnot
limit).
c.
If the actual Rankine cycle power output is 2.5 MW, calculate the
percentage of the Carnot limit the plant is achieving.
d.
Explain
physically
why
no
vapor
cycle
operating
temperature limits can exceed this power output.
between
these
Solutions: