ENGR 102/SPRING 2017/SECOND EXAM
Your Name: ___ Sample Answers _________
1. (16 points / important words): Define the following words and use each in a sentence:
a. Open system (when talking about thermodynamics)
Definition: ________Mass crosses boundaries_________________________________________
Give an example:__A car engine____________________________________________________
b. Dot product
Definition: _______A·B = ||A||*||B||cos(θ)_____________________________________________
Sentence: ________A cross product of two vectors will give a scalar result._________________
c. Mechanical work
Definition: _______Force x distance_________________________________________________
Sentence: ________The engine converted chemical energy to work,_______________________
d. Square matrix
Definition: _______Same number of rows and columns_________________________________
e.
f.
g.
h.
1 0
2 1
Give an example: ________________________________________________________________
Linear algebra
Definition: _______Mathematics of vectors and matrices_______________________________
Sentence: ________Linear algebra can solve systems of equations.________________________
Scalar
Definition: _______Has magnitude only______________________________________________
Sentence: ________Temperature and mass are scalar quantities._________________________
Unit (when talking about dimensions)
Definition: _______Quantification of a dimension______________________________________
Sentence: ________The meter is the SI unit for length.__________________________________
Editor (as used in MATLAB)
Definition: _______Place for writing MATLAB programs______________________________
Sentence: ________% is used at the beginning of a comment in the MATLAB Editor._______
2. (5 points). Energy storage. Give an example of each of the following types of stored energy:
a. Potential energy: ___Lifting a weight (or stretching a spring)__________________________
b. Kinetic energy: ___A car moving quickly on flat ground_____________________________
c. Internal energy: ___The heat content of steam from a furnace_________________________
d. Nuclear energy: ___Hydrogen atoms becoming helium atoms in the sun_________________
e. Chemical energy: __Burning gasoline in a car engine_________________________________
3. (4 points / matrices) Do the following matrix calculation. You calculate this manually showing
eaach step, but can use a calculator to check your result. Note that T means transpose.
A =
1 0
2 1
0 3
1 0
(1)(1)+(0)(0) (1)(2)+(0)(1) (1)(0)+(0)(3)
1 2 0
Calculate: A*AT = 2 1
= (2)(1)+(1)(0) (2)(2)+(1)(1) (2)(0)+(1)(3)
0 1 3
0 3
(0)(1)+(3)(0) (0)(2)+(3)(1) (0)(0)+(3)(3)
1 2 0
= 2 5 3
0 3 9
4. (30 points / thermodynamics and efficiency). In Qatar there are two options for cooling a building to
a temperature of 200C when the outside temperature is 400C.
Option 1. Bringing ice on a ship from Iceland. You can assume that:
 Ice is free in Iceland and the ice stays completely frozen on the well-insulated ship
 It takes a force of 14 N to move each ton (1.0 x103 kg). Otherwise the ship is 100% efficient
 The distance from Iceland to Qatar is 12 x103 km
 Converting 1.0 kg of ice to 1.0 kg of water at 20.00C will absorb 420 KJ
Option 2. Burning natural gas in a steam engine at a Carnot efficiency with a high temperature of
6400C that exhausts outside. The engine’s mechanical power then runs a perfectly (Carnot)
efficient heat pump (air conditioner). You can assume that: OK = OC + 273
a. (4 of 30 points) How much energy is needed to move 1 kg of ice from Iceland to Qatar?
Your answer:__ 170 KJ (2 sig digits)_______(make sure units and significant digits are correct)
Equation & calculation:
Work=(Force)(Distance)=(14N/1000kg)(12x106m)=168 000 Nm
b. (4 of 30 points) What is the refrigeration efficiency (useful cooling/work input) for Option 1?
Your answer:___2.5___________________ (make sure units and significant digits are correct)
Equation & calculation:
RE = (Useful cooling)/(work input)=(420 KJ)/(168 KJ)= 2.5
c. (4 of 30 points) What is the Carnot efficiency for the steam engine (Option 2)?
Your answer:____0.66________________ (make sure units and significant digits are correct)
Equation & calculation:
1-TL/TH = 1-(40+273)/(640+273) = 1-313/913 = 0.65717
d. (4 of 30 points) What is the refrigeration efficiency for the heat pump in Option 2?
Your answer:____15__________________ (make sure units and significant digits are correct)
Equation & calculation:
1/(TH/TL-1)= TL/(TH–TL)= (20+273)/(40-20) = 293/20 = 14.65
e. (4 of 30 points) What is the overall efficiency of the turbine+heat pump in Option 2?
Your answer:____9.6___________________ (make sure units and significant digits are correct)
Equation & calculation:
0.65717 x 14.65 = 9.6276
f.
(10 of 30 points) Draw the diagram to show the energy flows and systems for Option 2:
6400C
Energy from
natural gas
burning
Steam
Engine
400C
Waste
heat
Mechanical
work
Heat
Pump
400C
Waste
heat
200C
Useful
cooling
Building
5.
(20 points / concept understanding) Give the best answers you can to the following questions:
a. (4 points) Why would decreases in mass reduce the energy consumption of a car?
_____(1) Less energy needed to accelerate: (1/2)mv2 ___________________________________
_____(1) Less energy to go up hills: mgh ___________________________________________
b. (4 points) List two improvements that are needed to make electric cars more popular:
______(1) More energy per kg for battery, (2) Less expensive battery cost, (3) More places to
recharge battery, (4) Faster time to recharge battery, (5) Smaller battery _________________
c. (4 points) Explain the differences between standard of living and human development index:
_____ Standard of living: income __________________________________________________
_____ Human development index: income + life expectancy + education _________________
d. (8 points) List 4 places where you could get help to learn MATLAB:
_____(1) Help function in MATLAB_______________________________________________
_____(2) The internet____________________________________________________________
_____(3) Asking questions in class__________________________________________________
_____(4) Finding a textbook (in the library, for example)______________________________
6. (25 points total). The ideal gas law shows the relationship among properties of ideal gases:
PV = nRT
where: P = pressure (pascals)
V = volume (cubic meters)
n = number of moles of the ideal gas
R = universal gas constant: 8.314kJ/ (kmol K)
T = absolute temperature (OK) (note that OK = OC + 273)
Using the 7-step problem solving process learned in this class, calculate number of moles of air in
this room. You might need some of the following values:
Air pressure at 1600 meters = 83,900 N/m2
Temperature of this room: 21OC
Dimensions of this room: 7.0 x 10.0 x 4.0 meters
The mass of one mole of air is 28.97 g
To receive full credit, you must:
a. Show and label all of the steps in your process. (7 points)
b. Calculate the correct answer. (8 points)
c. Use the right number of significant digits in your answer. (5 points)
d. Have the correct units for your answer (5 points)
(You should use the separate blank next page to do this problem)
1. Problem statement
Find the number of moles of air in a rectangular 7 x 10 x 4.0 meter volume at a pressure of
83.9 kPa and 21OC temperature.
7.0 m
2. Diagram
Air at 83.9 kPa and
21OC temperature
2 Significant
4.0 m
10.0 m
3. Theory
Volume (V) for rectangular room is (Length)(Width)(Height)
For an ideal gas, the equation for number of moles (n) is : n = PV/RT
Temperature (T) conversion: T (in degrees K) = T (in degrees C) + 273
1 Pa = 1 N/m2
1 Joule = 1 Nm
4. Assumptions
(a) There are no people or objects in the room that occupy part of the gas volume
(b) The temperature is the same everywhere in the room
(c) The air is an ideal gas with R = 8.314kJ/ (kmol K)
5. Calculation steps
V = (7)(10)(4) = 280 m3
T = 21 + 273 = 294OK
n = PV/RT = (83,900 N/m2)(280 m3)/[(8.314 J/moles K)(294 K)]
n = [(83,900)(280)]/[(8.314)(294)] (moles)(Nm)/(J)
n = 9611
6. Result
9,600 moles of air in this room (2 significant digits)
7. Discussion
You do not need the mole weight of the air to solve this problem, but it is interesting to note that
the mass would be about (9,600 moles x 0.029kg) 280 kg (or about 4-5 students). This means
the students in a room weigh about 3-4x as much as the air in the room.