785
14.4 GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE
Math for Econ II, Written Assignment 2 (28 points)
Please write neat solutions for the problems below. Show all your work. If you only write the answer with no work,
you will not be given any cre

Chapter 4 Heat Effects.
(1) Sensible heat effects : heat transfer to or from a system : induce Tsystem change.
(2) Latent heat effects : heat transfer to or from a system : not induce Tsystem change
Ex) chemical reaction, phase transition, mixing, etc
Que

Vectors (10.2, 10.3 of Stewart)
Trush, Math for Economics II
January 23, 2015
Trush, Math for Economics II
Vectors (10.2, 10.3 of Stewart)
Foreshadowing directional derivatives: beyond fx and fy
The contour diagram of f (x, y ) below represents the temper

Directional derivatives, gradients, tangent planes,
and dierentials (11.4, 11.6 of Stewart)
Trush, Math for Economics II
February 4, 2015
Trush, Math for Economics II
Directional derivatives, gradients, tangent planes, and dierentials
Average rate of chan

ERC Working Papers in Economics 05/03
June 2005!
Fast Moving Consumer Goods
Competitive Conditions and Policies
Aydn elen
Competition Authority
Department III
Ankara Turkey
acelen@rekabet.gov.tr
Tarkan Erdo!an
Competition Authority
Department III
Ankara T

California High School
Exit Examination
Mathematics
Released Test Questions
California Department of Education
October 2008
2008 California Department of Education (CDE)
Permission is granted in advance for reproduction of these resources for educational

Chapter 6. Thermodynamic properties of fluids
Goals : 1) Find out relations among thermo properties
Ex)T, P, S, H, U, V, G, A
For F=2, if T and P are set, S, H, U, V, G and A are determined
automatically
There should exist relations amoung S, H, U, V, G

Chapter 5. The second law of thermodynamics
Entropy (S) state function, intensive property
dQ rev
dQrev
S t
T
T
t
Where S (total system entropy), T (system temperature)
t
For, dQrev = 0, S =0 isentropic process
dS t
dQ
dS t
surr
surr T
surr
Where
dQ
t

Chapter 2 THE FIRST LAW AND OTHER BASIC CONCEPTS
Question 2) (SVA 2.11) A tank containing 20 kg of water at 20 degree C is fitted with a stirrer that
delivers work to the water at the rate of 0.25 kW. How long does it take for the temperature of the
water

Chapter 3, Volumetric properties of pure flid
W, Q <-
U, H
<-
PVT relation
Question 8) (SVA 3.35 a, b) Determine Z(=PV/(RT) and V for steam at 250 oC and
1800 kPa by the following:
(a) The truncated virial equation[Eq. (3.40)] with the following experimen

Chapter 7. Thermodynamic of Flow processes
At steady state/steady flow and adiabatic conditions
Energy
Mass
Process
Energy
Mass
unit
Energy
Process unit : Pipe, nozzle, turbine, compressor, pump, etc
1. Pipe
Mass balance : m uA const
uA
const
V
0
0
u 2

Chapter 8. Heat engine (Q -> W by cyclic processes)
1
1. steam power plant
QH > 0, QC<0, W s(turbine) <0, W s(pump) > 0
2
1. Carnot engine - reversible
W>0
W<0
Energy balance :
W
net
W
W (exp ansion ) W (compression)
net
QH QC
3
2. The Rankine cycle
c.1

1. What is thermodynamics ?
1
Thermodynamics :
(a) Macroscopic : above
(b) Microscopic : molecular interactions -> generate (consume) energy -> converted into
other types of energy.
U
Intermolecular
distance
U : Intermolecular potential energy for a pair