Short Version : 18. Heat, Work, & First Law of Thermodynamics
18.1. The 1
st
Law of Thermodynamics
Either heating or stirring can raise
T
of the water.
Joule’s apparatus
1
st
Law of Thermodynamics
:
Increase in internal energy = Heat
added
Work done
Thermodynamic state variable
= variable independent of history.
e.g.,
U
,
T
,
P
,
V
, …
Not
Q
,
W
, …
PE
of falling weight
KE
of paddle
Heat
in water
18.2. Thermodynamic Processes
Quasi

static process
:
Arbitrarily slow process such that system always
stays arbitrarily close to thermodynamic equilibrium.
Reversible process
:
Any changes induced by the process in the universe (system
+ environment) can be removed by retracing its path.
Reversible processes must be quasi

static.
Irreversible process
:
Part or whole of process is not reversible.
e.g., any processes involving
friction, free expansion of gas ….
T
water
= T
gas
& rises slowly
system always in
thermodynamic equilibrium
Work & Volume Changes
面積
Work done by gas on piston
Isothermal Processes
Isothermal process
:
T
= constant.
Isothermal processes
on ideal gas
Constant

Volume Processes & Specific Heat
Constant

volume process
( isometric, isochoric, isovolumic ) :
V
= constant
C
V
= molar specific heat at constant volume
Ideal gas:
U = U
(
T
)
for all processes
isometric processes
only for isometric processes
Non

ideal gas:
Isobaric Processes & Specific Heat
Isobaric Process
: constant
P
isobaric processes
C
P
= molar specific heat at constant pressure
Ideal gas, isobaric :
Ideal gas
Isotherms
Adiabatic Processes
Adiabatic process
:
Q
= constant
e.g., insulated system, quick changes like combustion, …
Tactics 18.1.
adiabat
,
ideal gas
Prob. 66
Prob. 62
Adiabatic: larger
p
TACTIC 18.1
. Adiabatic Equation
Ideal gas, any process:
Adiabatic process:
Example 18.3
. Diesel Power
Fuel ignites in a diesel engine from the heat of compression (no spark plug needed).
Compression is fast enough to be adiabatic.
If the ignit temperature is 500
C, what compression ratio V
max
/ V
min
is needed?
Air’s specific heat ratio is
= 1.4, & before the compression the air is at 20
C.
Ideal Gas Processes
Cyclic Processes
Cyclic Process
: system returns to same thermodynamic state periodically.
Example 18.4
. Finding the Work
An ideal gas with
= 1.4 occupies 4.0 L at 300 K & 100 kPa pressure.
It’s compressed adiabatically to ¼ of original volume,
then cooled at constant
V
back to 300 K,
& finally allowed to expand isothermally to its original
V
.
How much work is done on the gas?
AB (adiabatic):
BC (isometric):
CA (
isothermal
):
work done by gas:
18.3. Specific Heats of an Ideal Gas
Ideal gas:
Experimental values
( room
T
):
For monatomic gases,
5/3, e.g.,
He, Ne, Ar,
….
For diatomic gases,
7/5 = 1.4, C
V
= 5R/2, e.g., H
2
, O
2
, N
2
, ….
For tri

atomic gases,
1.3, C
V
= 3.4R, e.g., SO
2
, NO
2
, ….
Degrees of freedom
(DoF) = number of independent
coordinates required to describe the system
Single atom: DoF = 3 (transl)
For low
T
( vib modes not active )
:
Rigid diatomic molecule : DoF = 5 (3 transl + 2 rot)
Rigid triatomic molecule : DoF = 6 (3 transl + 3 rot)
The Equipartition Theorem
Equipartition theorem
( kinetic energy version):
For a system in thermodynamic equilibrium, each degree of freedom of a
rigid molecule contributes ½
kT
to its average energy.
Equipartition theorem
( general version):
For a system in thermodynamic equilibrium, each degree of freedom described
by a quadratic term in the energy contributes ½
kT
to its average energy.
DoF (
f
)
C
V
C
P
Monatomic
3
3/2
5/2
5/3
Diatomic
5
5/2
7/2
7/5
Triatomic
6
3
4
4/3
Example 18.5
. Gas Mixture
A gas mixture consists of 2.0 mol of oxygen (O
2
) & 1.0 mol of Argon (Ar).
Find the volume specific heat of the mixture.
Quantum Effects
C
V
of H
2
gas as function of
T
.
Below 20 K hydrogen is liquid,
above 3200 K it dissociates into individual atoms.
Quantum effect
:
Each mechanism has a threshold energy.
E
transl
< E
rot
< E
vib
Translation
rotation+Translation
rotation+Translation+vibration
Reprise
Quasi

static process
:
Arbitrarily slow process such that system always stays arbitrarily close to thermodynamic equilibrium.
Reversible process
:
Any changes induced by the process in the universe (system + environment) can be removed
by retracing its path.
a
c : Free expansion with no dissipative work.
c
b
: Adiabatic.
a
d : Adiabatic.
d
b
: Free expansion with no dissipative work.
a
e : Adiabatic.
e
b
: Adiabatic dissipative work.
Insulated gas
1
st
law:
The net adiabatic work done in all 3 processes are
equal (shaded areas are equal).
Dissipative work
: Work done on system without changing its configuration, irreversible.
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