Download PS225 – Heat and thermodynamics

The First Law of
Thermodynamics
Thermodynamics
Very general: describes “working substances”
in terms of pressure, volume, temperature, ...
A thermodynamic system interacts with its
surroundings by exchange of heat, by doing
work, or both
A (macro)state describes the system, a process
makes the system go from one state to another
State variables
state variable: precisely measurable physical
property which characterizes the (macro)state
of a system, independent of how the system
was brought to that state
Examples: p, N, V, T, U
Any property that is a combination of state
variables is a state variable itself
Definitions
If the pressure is constant during a process, it
is said to be isobaric
V constant: isochoric
T constant: isothermal
no heat transfer: adiabatic/isentropic
p,V and p,T diagrams
It is often useful to plot p against V or p
against T in a graph. Which processes are
isothermal, isobaric, isochoric?
1
p
p
2
3
4
5
6
V
T
Changing internal energy
How can this be achieved?
by making the system do work W
by heating the system Q
W
Note signs:
W>0: work done by system
Q>0: heat flows into system
Q
reservoir
Work
Mechanics: if gas expands in the
direction of force F over distance
dx the work done is Fdx.
Write as function of pressure:
F=pA, dV=Adx so W = pdV
Integral form: W =  pdV
dV
A
F
dx
Work for different processes
Isochoric: V2 = V1 so W = 0
Isobaric: p is constant so
W
V2
V2
V1
V1
 pdV  p  dV  p(V2  V1)
Isothermal: p varies so we must write
W
V2
V2
V1
V1
 pdV  
V2
nRT
1
V2
dV  nRT  dV  nRT ln
V
V
V1
V
1
Process variables
Heat and work are variables associated with a
process. They are not state variables!
W   pdV  area under curve
p
1
p
W
V
2
1
W
V
2
The first law of
thermodynamics
Q = U + W
Warning! U:
ideal gas: kinetic energy only
real gas: small contribution from potential energy
Warning! W:
work done by gas expanding against pressure
mechanical work e.g. to lift piston
Internal energy is a state
variable
Experiments have shown:
Although neither Q nor W are state variables,
the internal energy is a state variable
In this sense the First Law of Thermodynamics
contains more than just conservation of energy
Question
An ideal gas expands by 20% of its
original volume. The work done does
not depend on
a) the mass of the piston
b) what gas is in this piston
c) the pressure inside the piston
d) the pressure outside the piston
Question
When ice melts at atmospheric pressure, its
volume decreases. The change in internal
energy is
a) greater than the heat added
b) equal to the heat added
c) less than the heat added
d) we can’t tell
Question
When water boils at atmospheric pressure, its
temperature remains 100 °C. This implies that
a) The kinetic energy of the molecules doesn’t
change
b) Most of the heat added is used to expand
c) The internal energy doesn’t change
d) No heat needs to be added to the system
PS225 – Thermal Physics
topics
The atomic hypothesis
Heat and heat transfer
Kinetic theory
The Boltzmann factor
The First Law of Thermodynamics
Specific Heat
Entropy
Heat engines
Phase transitions