Lecture 3 – The First Law (Ch. 1)
Friday January 11th
•Test of the clickers (HiTT remotes)
•I will not review the previous class
•Usually I will (certainly after Ch. 2)
•Internal energy
•The equivalence of work and heat
•The first law (conservation of energy)
•Functions of state
•Reversible work
Reading:
All of chapter 1 (pages 1 - 23)
1st homework set due next Friday (18th).
Homework assignment available on web page.
Assigned problems: 2, 6, 8, 10, 12
Functions of state: internal energy U
Adiabatic
Work = -DUgrav
W = -(-mgh)
= mgh
Joule’s paddle wheel
experiment
Measured as a change
in temperature, q
Gravitational energy is lost. 1st law is about conservation of energy. This
energy goes into thermal (‘internal’) energy associated with the fluid.
Functions of state: internal energy U
Adiabatic
DUfluid = W = mgh
!!!!!!!!!!!!!!!!!!!!!!!
Joule’s paddle wheel
experiment
Measured as a change
in temperature, q
Gravitational energy is lost. 1st law is about conservation of energy. This
energy goes into thermal (‘internal’) energy associated with the fluid.
Functions of state: internal energy U
Stirring
Adiabatic
Rise in q
(temperature)
DU = W = torque × angular displacement = t df
Functions of state: internal energy U
Electrical
work
Adiabatic
Rise in q
(temperature)
i
R
DU = W =
2
i R
Functions of state: internal energy U
Reversible
work
Force, F
Adiabatic
Rise in q
(temperature)
DU = W = Force × distance = -P DV
Equivalence of work and heat
Heat, Q
Adiabatic
Same rise in q
(temperature)
DU = Q
The First Law of Thermodynamics
These ideas lead to the first law of thermodynamics (a
fundamental postulate):
DU = Q + W
or
dU = đQ + đW
“The change in internal energy of a system is
equal to the heat supplied plus the work done
on the system. Energy is conserved if the
heat is taken into account.”
Note that đQ and đW are not functions of state. However,
dU is, i.e. the correct combination of đQ and đW which, by
themselves are not functions of state, lead to the
differential internal energy, dU, which is a function of
state.
How to know if quantity is a function of state
U1
W   PdV  area under curve
Significant
heat flows in
U2
How can U be state function, but not W?
Heat is involved (not adiabatic).
DU   đQ + đW 
How to know if quantity is a function of state
There is a mathematical basis.....
Consider the function F = f(x,y):
 f 
 f 
dF    dx +   dy
 x  y
 y  x
z
dS
y

dF
x
dr
How to know if quantity is a function of state
There is a mathematical basis.....
Consider the function F = f(x,y):
 f 
 f 
dF    dx +   dy
 x  y
 y  x
In general, F is a state function if the differential dF is
‘exact’. dF (= Adx + Bdy) is exact if:
1.
2.
A B

y x
See also:
•Appendix E
•PHY3513 notes
•Appendix A in Carter book
 dF  0
 dF is independent of path
b
3.
a
•In thermodynamics, all state variables are by definition
exact. However, differential work and heat are not.
How to know if quantity is a function of state
Differentials satisfying the following condition are said to
be ‘exact’:

dF  0
This condition also guarantees that any integration of dF
will not depend on the path of integration, i.e. only the
limits of integration matter.
This is by no means true for any function!
If integration does depend on path, then the differential is
said to be ‘inexact’, i.e. it cannot be integrated unless a
path is also specified. An example is the following:
đF = ydx - xdy.
Note: is a differential đF is inexact, this implies that it
cannot be integrated to yield a function F.