Transcript Slide 1

Thermodynamics
Thermodynamic Systems, States and
Processes
Objectives are to:
• define thermodynamics systems and states of systems
• explain how processes affect such systems
• apply the above thermodynamic terms and ideas to the laws of
thermodynamics
Internal Energy of a Classical ideal gas
“Classical” means Equipartition Principle applies: each
molecule has average energy ½ kT per in thermal equilibrium.

At room temperature,
for most gases:
3
KE  kT
2
monatomic gas (He, Ne, Ar, …)
3 translational modes (x, y, z)
diatomic molecules (N2, O2, CO, …)
3 translational modes (x, y, z)
+ 2 rotational modes (wx, wy)
UN
3
3
kT  pV
2
2
5
KE  kT
2
Internal Energy of a Gas
A pressurized gas bottle (V = 0.05 m3), contains
helium gas (an ideal monatomic gas) at a pressure p =
1×107 Pa and temperature T = 300 K. What is the
internal thermal energy of this gas?
3
3
U  N kT  pV
2
2



 1.5  107 Pa  0.05m3  7.5 105 J
Changing the Internal Energy

U is a “state” function --- depends uniquely on the state of the
system in terms of p, V, T etc.
(e.g. For a classical ideal gas, U = NkT )

There are two ways to change the internal energy of a system:
WORK done by the system
on the environment
Wby = -Won
HEAT is the transfer of thermal energy
into the system from the surroundings
Thermal reservoir
Q
Work and Heat are process energies, not state functions.
Work Done by An Expanding Gas
The expands slowly enough to
maintain thermodynamic equilibrium.
dW  Fdy  PAdy
Increase in volume, dV
dW  PdV
+dV Positive Work (Work is
done by the gas)
-dV Negative Work (Work is
done on the gas)
A Historical Convention
+dV Positive Work (Work is
done by the gas)
Energy leaves the system
and goes to the environment.
-dV Negative Work (Work is
done on the gas)
Energy enters the system
from the environment.
Total Work Done
dW  PdV
Vf
W   PdV
Vi
To evaluate the integral, we must know
how the pressure depends (functionally)
on the volume.
Pressure as a Function of Volume
Vf
W   PdV
Vi
Work is the area under
the curve of a PV-diagram.
Work depends on the path
taken in “PV space.”
The precise path serves to
describe the kind of
process that took place.
Different Thermodynamic Paths
The work done depends on the initial and final
states and the path taken between these states.
Work done by a Gas


When a gas expands, it does work on its environment
Consider a piston with cross-sectional area A
filled with gas. For a small displacement dx,
the work done by the gas is:
dWby = F dx = pA dx = p (A dx)= p dV
 We generally assume quasi-static processes (slow
enough that p and T are well defined at all times):
dx
Wby 
This is just the area under the p-V curve
p
 p dV
Vi
p
p
V
Vf
V
V
Note that the amount of work needed to take the system from one
state to another is not unique! It depends on the path taken.
What is Heat?

Up to mid-1800’s heat was considered a substance -- a
“caloric fluid” that could be stored in an object and
transferred between objects. After 1850, kinetic
theory.

A more recent and still common misconception is that
heat is the quantity of thermal energy in an object.

The term Heat (Q) is properly used to describe energy
in transit, thermal energy transferred into or out of a
system from a thermal reservoir …
Q

U
(like cash transfers into and out of your bank account)
Q is not a “state” function --- the heat depends on the
process, not just on the initial and final states of the system
Sign of Q :
Q > 0 system gains thermal energy
Q < 0 system loses thermal energy
An Extraordinary Fact
The work done depends on the initial and final
states and the path taken between these states.
BUT, the quantity Q - W does not depend
on the path taken; it depends only on the initial
and final states.
Only Q - W has this property. Q, W, Q + W,
Q - 2W, etc. do not.
So we give Q - W a name: the internal energy.
The First Law of Thermodynamics
(FLT)
-- Heat and work are forms of energy transfer
and energy is conserved.
U = Q + Won
change in
total internal energy
heat added
to system
State Function
work done
on the system
Process Functions
or
U = Q - Wby
1st Law of Thermodynamics
U  Q  W
positiveQ : heat added to system
positiveW : work done by system
• statement of energy conservation for a thermodynamic
system
• internal energy U is a state variable
• W, Q process dependent
The First Law of Thermodynamics
dEint  dQ  dWby
What this means: The internal energy of a system
tends to increase if energy is added via heat (Q)
and decrease via work (W) done by the system.
dEint  dQ  dWon
. . . and increase via work (W) done on the system.
dWby  dWon
Isoprocesses
• apply 1st law of thermodynamics to closed
system of an ideal gas
• isoprocess is one in which one of the
thermodynamic (state) variables are kept
constant
• use pV diagram to visualise process
Isobaric Process
• process in which pressure is kept
constant
Isochoric Process
• process in which volume is kept
constant
Isothermal Process
• process in which temperature is held
constant
Thermodynamic processes of an ideal gas
( FLT: U = Q - Wby )

Isochoric (constant volume)
Wby   pdV 0
U   Nk T   V p
FLT:
2
p
Q  U
Q
1
Temperature
changes
V

Isobaric (constant pressure)
Wby   pdV  pV
U   Nk T   p V
FLT: Q  U  Wby    1 p V
p
1
2
p
Q
V
Temperature and
volume change
( FLT: U = Q - Wby )

Isothermal (constant temperature)
U  0
p
1
V2
V2
Wby   p dV  NkT n
V1
V
2
p
Q
1
FLT:
1
V
Thermal Reservoir
Q Wby
V
T
Volume and
pressure change