1. Thermodynamics

2. 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

3. At room temperature, for most gases:
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:
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)
Note: At higher temps, other modes can come in, e.g., vibrational modes.

4. 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?

5. 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 Q
Thermal reservoir
Work and Heat are process energies, not state functions.

6. Work Done by An Expanding Gas
The expands slowly enough to
maintain thermodynamic equilibrium.
Increase in volume, dV
+dV Positive Work (Work is
done by the gas)
-dV Negative Work (Work is
done on the gas)

7. A Historical Convention
+dV Positive Work (Work is
done by the gas)
-dV Negative Work (Work is
done on the gas)
Energy leaves the system
and goes to the environment.
Energy enters the system
from the environment.

8. Total Work Done To evaluate the integral, we must know
how the pressure depends (functionally)
on the volume.

9. Pressure as a Function of Volume
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.

10. Different Thermodynamic Paths
The work done depends on the initial and final
states and the path taken between these states.

11. Work done by a Gas dWby = F dx = pA dx = p (A dx)= p dV dx
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: dx
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):
This is just the area under the p-V curve V p p V p 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.

12. 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 …
(like cash transfers into and out of your bank account) Q U
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

13. 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.

14. 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
work done
on the system
State Function Process Functions or
U = Q - Wby

15. 1st Law of Thermodynamics
statement of energy conservation for a thermodynamic system
internal energy U is a state variable
W, Q process dependent

16. The First Law of Thermodynamics
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.
. . . and increase via work (W) done on the system.

17. 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

18. Isobaric Process
process in which pressure is kept constant

19. Isochoric Process
process in which volume is kept constant

20. Isothermal Process
process in which temperature is held constant

21. Thermodynamic processes of an ideal gas ( FLT: DU = Q - Wby )
Isochoric (constant volume) V p 1 2 Q
Temperature changes
FLT:
Isobaric (constant pressure) V p 1 2
FLT: Q
Temperature and volume change

22. Isothermal (constant temperature)
( FLT: DU = Q - Wby )
Isothermal (constant temperature) Q
Thermal Reservoir T
Volume and pressure change p V 1 2
FLT: