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First Name ___________________Last Name ____________________ CIRCLE YOUR LECTURE BELOW: Div. 1 – 08:30 am Div. 2 – 11:30 am Prof. Chen Prof. Braun EXAM # 1

INSTRUCTIONS 1. This is a closed book examination. You are allowed to have a single sheet of 8.5 in. x 11 in.

paper with notes on both sides for the examination. All needed property tables are provided. 2. Do not hesitate to ask the instructor if you do not understand a problem statement. 3. Start each problem on the same page as the problem statement. Write on only one side of the

page. Materials on the back side of the page will not be graded. There are blank pages following each of the second and third problems for your work.

4. Put only one problem on a page. A second problem on the same page will not be graded. 5. If you give multiple solutions, you will receive only a partial credit although one of the

solutions is correct. Delete the solutions you do not want. 6. For your own benefit, please write clearly and legibly. Maximum credit for each problem is

indicated below. 7. After you have completed the exam, at your seat, put your papers in order. This may mean

that you have to remove the staple and re-staple. Do not turn in loose pages. 8. Once time is called you will have three minutes to turn in your exam. Points will be

subtracted for exams turned in after these three minutes.

Problem Possible Score

1 20

2 35

3 45

Total 100

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First Name ___________________Last Name ____________________ Problem 1. (20 points) This problem consists of 10 parts. Each part is 2 points. Place your brief answers in the boxes.

a) A cup of coffee gets colder in a room. Will the kinetic energy in the coffee become larger, smaller, or remain the same.

b) A refrigerator has been working steadily in a well-insulated room

for a long time with the refrigerator door always opened. Will the room air temperature increase, decrease, or remain the same?

c) Water is compressed from 1 atm to 10 atm. Neglect kinetic and potential energy changes. Which one would need more work input, water liquid or water vapor?

d) Can the entropy change of a system undergoing a process be negative?

e) Is there any entropy generation in a Carnot heat engine?

f) A furnace burning heating oil at 500oC could be used for a process requiring 120oC steam or to heat hot water at 70oC for use in a home. Which has higher exergetic (2nd law) efficiency?

g) Is the following second law efficiency equation for a turbine or a compressor?

( )cv fW / m eε = Δ

h) Is it possible for exergy to be negative?

i) Is the exergy of a system different in different environments? j) System A is at the same temperature as the environment, whereas

System B is at a lower temperature than the environment. Which system has higher specific exergy?

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First Name ___________________Last Name ____________________ Problem 2. (35 points) Consider a horizontal rigid cylinder of which the wall and one end is well insulated. The cylinder is divided into two compartments by a piston that is free to move but does not allow either gas to leak into the other side. Initially, one side of the piston contains 0.1 m3 of oxygen (O2) gas at 400 kPa and 200oC while the other side contains 0.1 m3 of helium (He) gas at 400 kPa and 0oC. The piston is made of a piece of rigid material that has very high heat conductivity. Neglect the friction of the piston movement, energy change in the cylinder walls, and energy change in the piston. Now thermal equilibrium is established in the cylinder as a result of heat transfer through the piston and the heat transfer between the un-insolated end wall of the helium chamber and the environment at 30oC and 100 kPa. The final temperature in the cylinder is the same as the environment temperature and the final pressure in both of the chambers 314 kPa. Using constant specific heat provided below, determine: a) The total heat transfer from the cylinder end to the environment, in kJ. b) The direction of the heat transfer (the cylinder to the environment or the environment to the

cylinder) c) The exergy of oxygen gas at its initial state, in kJ d) The total exergy destruction for the process, in kJ R =8.314 kJ/kmol K, Cv,O2 = 0.668 kJ/kgK, Cv,He = 3.115 kJ/kgK, Cp,O2 = 0.928 kJ/KgK, Cp,He = 5.1926 kJ/kgK, MO2 = 32 kg/kmol, MHe = 4 kg/kmol Please circle your answers.

Assumptions:

O2, 0.1 m3, 400 kPa, 200oC

He, 0.1 m3, 400 kPa, 0oC

Copper Insulation

Q To = 30oC Po = 100 kPa

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First Name ___________________Last Name ____________________ Solution:

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First Name ___________________Last Name ____________________ Problem 3. (45 points) A 4 liter pressure cooker has an operating pressure of 200 kPa when it is placed on a stove at a temperature of 1000oC. The environment temperature is 20oC. The heat loss from the cooker to the environment through the cooker wall and lid is 300 W. Initially, one-half of the volume is filled with liquid and the other half with vapor. Neglect the kinetic energy and potential energy. Assume that the temperature and pressure are uniform throughout the cooker and heat is added at a fixed rate from the stove. If the pressure cooker runs out of liquid water after one hour, determine a) The total mass of the steam entering the

environment, in kg b) The rate of heat transfer from the source,

in kW c) The total entropy production in one hour

within the control volume shown, in kJ/K d) The total exergy destroyed in one hour for the control volume shown, in kJ Please circle your answers. Assumptions: Solution:

1000oC

Steam vapor

Liquid water

Water vapor

V= 4 liter

inQ

loss

oo

Q 300W

T 20 C

=

=

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