1. The First Law of Thermodynamics

2. 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

3. 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

4. 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

5. 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 4 2 5 3 6 V T

6. Changing internal energy
How can this be achieved?
by making the system do work W
by heating the system Q
Note signs:
W>0: work done by system
Q>0: heat flows into system W Q
reservoir

7. 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

8. Work for different processes
Isochoric: V2 = V1 so W = 0
Isobaric: p is constant so
Isothermal: p varies so we must write

9. Process variables
Heat and work are variables associated with a process. They are not state variables! 1 1 p p W 2 2 W V V

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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