Download Guided Practice Problems- Exam 3

ME 200 Thermodynamics – Spring 2016
PREPARING FOR EXAM 3
I. Class Notes, Examples and Quizzes
Review all class notes, examples and quizzes from Lectures 1 - 34. Do you understand all of the
concepts that were presented and discussed? Could you solve the examples and quizzes without
looking at the solutions?
II. Homework Problems
Be able to solve all of the special problems until Lecture 34 (SP1 – SP34) without having to look
at the solutions. Do all of the supplemental text problems listed on the syllabus that are assigned
through Lecture 34. Solutions for SP1 – SP34 and an answer key for the supplemental text
problems are provided on Blackboard for each section.
III. Old Exams
The ME 200 website (https://engineering.purdue.edu/ME200/) has previous exams (Exam 3) for
Fall 2011 and Spring 2013. Try to solve the old exams in the time normally allotted for a onehour exam. There also is a posted solution for Exam 3 from last semester. You can review this
but it would better if you tried to solve it without looking at the solution.
IV. Some Additional Practice Problems
1. A small air conditioner cools a space at 20oC at a rate of 2.5 kW and rejects heat to the
outdoors at a temperature 35oC. What is the rate of entropy production for a COP of 5?
2. An inventor claims that a process produces a work output that is equal to the heat input when
going from one state to another. Does this claim violate the Kelvin-Planck Statement of the
2nd Law? Explain.
3. An engineer has devised a system that employs a heat engine
(HE) and heat pump (HP) and produces a net power output
( W net ) as depicted. Is this net power delivery rate possible for
the given conditions? Justify your answer using an entropy
balance with calculations.
High Temperature Reservoir
@ 300 C
HP
increases
increases
increases
increases
increases
increases
increases
increases
increases
increases
HE
Wnet  100 kW
Q M ,HP  500 kW
Medium Temperature
Reservoir @ 50C
4. Does entropy increase, decrease, or remain constant for each
case? Justify with property relations or entropy balances.
Ideal gas with constant P and increasing v
Incomp. liquid with constant T and decreasing P
Incomp. liquid with constant h and decreasing P
Ideal gas with constant h and decreasing P
2-phase mixture with constant h and decreasing P
Ideal gas undergoing an isothermal compression
2-phase substance condensed at constant pressure
Closed system undergoing a rev. adiabatic process
Closed reversible system undergoing heat rejection
Adiabatic, irreversible process
Q H ,HE  1000 kW
Q H ,HP  1000 kW
Low Temperature
Reservoir @ -50C
decreases
decreases
decreases
decreases
decreases
decreases
decreases
decreases
decreases
decreases
same
same
same
same
same
same
same
same
same
same
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5. Heat transfer at a rate of 10 kW is needed for a process operating at
300 K. How would the total rate of entropy generation change
with increasing temperature of the heat source for the same heat
transfer rate? a) increases, b) decreases, c) doesn’t change, d) can’t
tell. Utilize an entropy balance to justify.
Source at TH
Q  10 kW
Process at 300 K
6. Liquid water treated as an incompressible fluid is flowing through a horizontal, adiabatic,
and internally reversible diffuser. What happens to the following quantities as the water
flows through the device? Use basic equations to justify.
Velocity:
Enthalpy:
Entropy:
Temperature:
Pressure:
increases
increases
increases
increases
increases
decreases
decreases
decreases
decreases
decreases
constant
constant
constant
constant
constant
7. Refrigerant enters an adiabatic and irreversible throttling valve as a saturated liquid where it
is throttled to a low pressure and then evaporated inside a heat exchanger at constant pressure
before it exits as a saturated vapor. Depict the process that the refrigerant undergoes on a T-s
Heat Exchanger
diagram with respect to the
3
1 Throttle 2
dome, showing the individual
Saturated
Saturated
Liquid at
Vapor at
state points that are indicated
X
High Pressure
Low
Pressure
in the figure below.
8. A steady stream of air is compressed adiabatically to a higher pressure. Would the exit
temperature from the compressor be higher for a reversible or irreversible compressor for the
same inlet condition and exit pressure? Explain why. Depict on a T-s diagram.
9. Is there any circumstance where an irreversible process could ever be isentropic?
entropy balance to justify.
Use an
10. Consider a piston-cylinder device with 1 kg of air initially at a temperature 20oC and a
pressure of 2 bar. It has been claimed that after a total of 25 kJ of heat has been transferred
to the air in a constant pressure process, the final temperature is 30oC. The temperature of
the source of the heat addition is 300oC. Using this data, determine: a) the specific work
done by the air and b) whether the stated process and conditions violate sat. water vapor
the 2nd Law.
at P1 = 5 MPa
11. Saturated water vapor at 5 MPa enters an adiabatic throttle and exits at 1.5
MPa. What is the entropy production per unit mass of water vapor
flowing? What if the throttle were replaced with an adiabatic and
reversible turbine? Depict the two processes on a T-s diagram with
respect to the dome and constant pressure lines.
1
2
P2 = 1.5 MPa
2
12. An inventor claims to have devised a steady-flow compressor, which requires no shaft-power
input. It is claimed that CO2 at 15 bar and 50oC can be compressed to 20 bar, where it will
emerge at -5oC, simply by a transfer of energy as heat from this device. The patent
application states that the device will handle 2 kg CO2 per second and is driven by a “cold
source” at –95oC (-140oF). They further
state that the CO2 enters and leaves the
device at very low velocity, and that no Inlet
Outlet
significant elevation changes are involved.
Can these claims be valid? Assume ideal
gas but allow for variable specific heats.
Heat Transfer
Depict the process on a T-s diagram
showing constant pressure lines.
-140 F
13. At steady state, steam with a mass flow
rate of 5 kg/s enters a turbine at 400oC and 40 bar and expands to 4 bar. The power
developed by the turbine is 2127 kW. The steam then passes through a heat exchanger with a
negligible change in pressure, exiting at 400oC. Air enters the heat exchanger in a separate
stream at 1.4 bar, 550oC and exits at 1.2 bar, 325oC. Determine the total rate of entropy
production. Neglect changes in kinetic and potential energy and assume the turbine is
adiabatic.
14. A 1 kg piece of copper at 30oC is dropped in a large
lake that is at 15oC. Determine the total entropy
production. (Assume that the copper has a constant
specific heat of 0.39 kJ/kg-K and treat the lake as a
reservoir at constant and uniform temperature.)
Lake
Copper Block
15. Liquid water flowing in a pipe at a rate of 0.12 kg/s is heated using an electrical resistance
heater as depicted below. At steady flow and steady state conditions, electrical power is
dissipated in the resistor at a rate of 10 kW and heats the water from 15C to 35C with
negligible change in water pressure. The resistor is at a uniform and constant temperature of
50C. The pipe is approximately adiabatic and changes in kinetic and potential energy are
negligible. Water can be treated as an incompressible substance with a constant specific heat
of 4.18 kJ/kg-K. With this information, do the following:
a) Determine the total rate of entropy generation for this process, in kW/K.
b) Determine the rate of entropy generation for the water alone, in kW/K.
c) Determine the rate of entropy generation for the resistor alone, in kW/K.
For each part, you need to show your system, list assumptions, and start with basic
equations.
T = 50C
Water: 0.12 kg/s
T1 = 15C
P1 = 300 kPa
+
10 kW
T2 = 35C
P2 = 300 kPa
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16. Two liquid water streams are mixed together in a steady-state, steady-flow process at
constant pressure. One stream has a temperature of 60oC and mass of flow rate of 1 kg/s,
while the other enters at 10oC and 0.1 kg/s. Heat transfer occurs to an environmental
temperature of 20oC, such that the exit temperature of the liquid water is 48oC. Determine
the rate of entropy production. Neglect changes in kinetic & potential energy.
17. Air enters a nozzle at 4 bar, 277oC, and 60 m/s and exits at 0.75 bar. Assuming ideal gas
behavior, variable specific heats and a reversible and adiabatic process, determine the exit
temperature of the air.
18. Air is expanded reversibly in a closed piston-cylinder from an initial state of 0.05 m3, 10 bar,
and 600K to a final pressure of 2 bar. The piston is located in an environment of 25C.
Determine the expansion work (kJ) for two cases: a) adiabatic expansion (assume variable
specific heats) and b) isothermal expansion (assume constant specific heats).
19. As shown below, a turbine is located between two tanks. Initially, the smaller tank contains
air at 3.0 MPa and 280C within a volume of 100 m3. The larger tank is evacuated and has a
volume of 1000 m3. The air then flows from the smaller tank, through the turbine, and into
the larger tank until equilibrium is attained. Determine the maximum work output (kJ) if
there are no irreversibilities. Show your system, list assumptions, and start with basic
equations.
Initially: air
at 3 MPa, 280C
Initially evacuated
Turbine
100 m3
1000 m3
Hints: Choose a system that remains
closed
throughout
the
process!
Calculate specific volumes before and
after.
The volume of the turbine and piping is
negligible, and heat transfer to the
surroundings is negligible. Air at these
conditions can be treated as an ideal gas,
but you must consider the temperature
dependence of specific heats.
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