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Department

Mechanical Engineering

Course Code

MECHENG 235

Professor

Donald Siegel

Description

ME 235 FINAL EXAM, December 16, 2011
K. Kurabayashi and D. Siegel, ME Dept.
Exam Rules: Open Book and one page of notes allowed. There are 4 problems. Solve each
problem on a separate page.
Name: __________________________________
I have observed the honor code and have neither given nor received aid on this exam.
Signature:____________________________________________
3
Problem 1. (25 points) A 0.2 m rigid container is initially empty, and connected to a supply line
providing superheated water vapor at 500 kPa, 200 °C (see figure below). When the valve
connecting the line and container is opened the container is filled from the supply line. When the
flow stops, the pressure in the container is the same as the pressure in the line. Assume the
process is adiabatic.
a) Write appropriate expressions for the continuity, energy and entropy equations
b) What is the final temperature of water in the container?
c) Find the final mass of the water in the container.
d) Find the entropy generation in the process.
Line
200°C Container
500
kPa 0.2
m
Problem 2. (25 points) A 2.4 L gasoline engine runs at 2500 RPM with a compression ratio of
9:1. The state before compression is 40 kPa, 280 K and after combustion it is at 2000 K. Assume
a 4-stroke Otto cycle. You may use constant specific heats for air. Determine:
a) The highest T and P in the cycle
b) The specific heat transfer added
c) The cycle efficiency
d) The exhaust temperature
Problem 3. (25 points) A heat pump upgrades 5 MW of heat at 85 C to heat delivered at 150 C. o
Assume it has a COP of 2.5.
a.) Write appropriate expressions for the energy and entropy equations.
b.) Determine the rate of work input and the rate of heat delivery.
c.) What are the fluxes of entropy into and out of the heat pump?
d.) What is the rate of entropy generation inside the heat pump?
1
Problem 4 (25 points) Choose the correct answer for each problem. Write down the process of
reaching your answer for partial credit.
(1) [3 pts] A piston-cylinder device contains 5 kg of air at 400 kPa and 30 °C. During a
quasi-equilibrium isothermal expansion process, 15 kJ of boundary work is done by the
system, and 3 kJ of paddle-wheel work is done on the system. The heat transfer during
this process is
(a) 12 kJ (b) 18 kJ (c) 2.4 kJ (d) 3.5 kJ (e) 60 kJ
(2) [3 pts] In a shower, cold water at 10°C steadily flowing at a rate of 5 kg/min is mixed
with hot water at 60°C steadily flowing at a rate of 2 kg/min. The exit temperature of the
mixture is
(a) 24.3 °C (b) 35.0 °C (c) 40.0 °C (d) 44.3 °C (e) 55.2 °C
(3) [3 pts] A unit mass of a substance undergoes an irreversible process from state 1 to state
2 while gaining heat from the surroundings at temperature T in the amount of q. If the
entropy of the substance is s 1t state 1, and s at2state 2, the entropy change of the
substance Δs during this process is
(a) Δss − (c) Δs=s − (d) Δs=s −qT+
2 1 2 1 2 1 2 1
(e) Δ>s −q2 1
(4) [3 pts] Consider a simple ideal Rankine cycle. If the condenser pressure is lowered while
keeping turbine inlet state the same, choose all the correct statements among the
following.
(a) the pump work input will decrease (b) the pump work input will increase
(c) the turbine work output will decrease (d) the turbine work output will increase
(e) the moisture content (i.e., the amount of liquid water) at turbine exit will increase
3
(5) [13 pts] A thermally insulated rigid container with a volume of 1.0 m is divided into two
equal volumes by a partition. Initially, only one side of the container is filled with
nitrogen (ideal gas) at 600 kPa, 127°C. The partition ruptures, and the nitrogen fills the
both sides at a uniform state.
(5-1) [2 pts] This process is
(a) Irreversible due to heat transfer (b) Irreversible due to friction (c) Irreversible due
to unrestrained expansion, (d) Irreversible due to fluidic work, (e) Reversible
(5-2) [4 pts] The final temperature is
(a) 200K (b) 300K (c) 400K (d) 500K (e) 600K
(5-3) [3 pts] The final pressure is
(a) 150 kPa (b) 200 kPa (c) 250 kPa (d) 300 kPa (e) 600 kPa
(5-4) [4 pts] The entropy generated by this process is
(a) 0 kJ/K (b) 0.11 kJ/K (c) 0.24 kJ/K (d) 0.43 kJ/K (e) 0.52 kJ/K
2
Solutions:
Problem 1.
C.V. The container volume and any valve out to line.
Continuity Eq: m - m 2 m =1m 2 i
Energy Eq: m u -2 2u = m1 1= Q - 2 2 mh1= 2h 1 2 i i i i
Entropy Eq: m s - 2 2 = m1 1= 2 2 δQT + S1 2n + ms i i
∫
Process: Adiabatic Q 1 02 Rigid W = 0,1Flo2 stops P = Pline 2

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