1.
a) Use the Chain Rule to calculate the partial derivatives.
Express the answer in terms...
1.
a) Use the Chain Rule to calculate the partial derivatives.
Express the answer in terms of the independent variables.
∂f
∂r
∂f
∂t
; f(x, y, z) = xy +
z2, x = r + s −
2t, y = 6rt, z =
s2
∂f
∂r
=
∂f
∂t
=
b) Use the Chain Rule to calculate the partial derivative.
Express the answer in terms of the independent variables.
∂F
∂y
; F(u, v) =
eu+v, u =
x5, v = 2xy
∂F
∂y
=
c)...
Derive an expression for β =
1/V(∂V/∂T)P for such a gas in
terms of b(T) ,...
Derive an expression for β =
1/V(∂V/∂T)P for such a gas in
terms of b(T) ,
db(T)/dT , P
, and Vm .
Express your answer in terms of the variables
b(T) ,
db(T)/dT , P
, and Vm .
Express the following in terms of αp, βT, Cv, Cp, S, V, T,
P.
∂G/∂P at...
Express the following in terms of αp, βT, Cv, Cp, S, V, T,
P.
∂G/∂P at constant S.
a.The derivative (∂V/∂T)P is tedious to calculate by
implicit differentiation of an equation of state such...
a.The derivative (∂V/∂T)P is tedious to calculate by
implicit differentiation of an equation of state such as
the Peng-Robinson equation. Show that calculus
permits us to find the derivative in terms of derivatives
of pressure, which are easy to find, and provide the
formula for this equation of state.
b. Using the Peng-Robinson equation, calculate the
isothermal compressibility of ethylene for saturated
vapor and liquid at the following conditions: {Tr = 0.7,
P = 0.414 MPa}; {Tr = 0.8, P...
2. Let A = {p, q, r, s}, B = {k, l, m, n}, and C...
2. Let A = {p, q, r, s}, B = {k, l, m, n}, and C = {u, v, w},
Define f : A→B by f(p) = m, f(q) = k, f(r) = l, and f(s) = n, and
define g : B→C by g(k) = v, g(l) = w, g(m) = u, and g(n) = w. Also
define h : A→C by h = g ◦ f. (a) Write out the values of h. (b) Why
is it that...
Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and
?=3?+2?v=3i+2j.
A. Find the gradient of f.
∇?=∇f= ?+i+ ?j
Note: Your answers should...
Suppose ?(?,?)=??f(x,y)=xy, ?=(−4,−4)P=(−4,−4) and
?=3?+2?v=3i+2j.
A. Find the gradient of f.
∇?=∇f= ?+i+ ?j
Note: Your answers should be expressions of x and y; e.g. "3x -
4y"
B. Find the gradient of f at the point P.
(∇?)(?)=(∇f)(P)= ?+i+ ?j
Note: Your answers should be numbers
C. Find the directional derivative of f at P in the direction of
?v.
???=Duf=
D. Find the maximum rate of change of f at P.
E. Find the (unit) direction vector in which the maximum rate...
Suppose that an economy is characterized by M = $10 trillion, V
= 2, P =...
Suppose that an economy is characterized by M = $10 trillion, V
= 2, P = base index = 1.0
Instructions: Enter your responses rounded to two decimal places
(do not include a negative sign (-) with your answers).
a. What is the real value of output (Q)?
Now assume that the Fed increases the money supply by 20 percent
and velocity remains unchanged.
b. If the price level remains constant, by how much will real
output increase?
c. If,...
Constants
The following values may be useful when solving this
tutorial.
Constant
Value
E∘Cu
0.337 V...
Constants
The following values may be useful when solving this
tutorial.
Constant
Value
E∘Cu
0.337 V
E∘Ni
-0.257 V
R
8.314 J⋅mol−1⋅K−1
F
96,485 C/mol
T
298 K
Part A
In the activity, click on the E∘cell and Keq
quantities to observe how they are related. Use this relation to
calculate Keq for the following redox reaction that occurs
in an electrochemical cell having two electrodes: a cathode and an
anode. The two half-reactions that occur in the cell are...