1. In 1-D only one way to integrate this.
The fundamental theorem of calculus: f = f(x)
In 1-D only one way to integrate this.

2. In 2-D infinite paths possibley
z = z(x,y) A C x a b
For an exact differential

3. Green’s theorem y A C x a b

4. Is path independent e.g. state variables, P = P(V,T)
In general, the differential dz = Mdx + Ndy is ‘exact’ if:
Is path independent
e.g. state variables, P = P(V,T)

5. Inexact differentials do not satisfy these conditions
e.g. dz = ydx - xdy
Sum of two inexact differentials can be exact.

6. First law of thermodynamics (in words)
Heat: Spontaneous flow of energy caused by the temperature difference between two objects
Work: Any other kind of energy transfer
Internal Energy: Total energy in a system
First law of thermodynamics (in words)
Increase in internal energy = Heat added + work done on the system
U = Q + W
(W is the work done ON the system)

7. First law of thermodynamics (in words)
Increase in internal energy = Heat added + work done on the system
U = Q + W
(W is the work done ON the system)
Phlogiston?

8. First law of thermodynamics
dQ = dU - dW
Show PdV

9. Configuration Work
This is the work done in a reversible process given by the product of some intensive variable (y) and the change in some extensive variable (X). The most general case would be:
đW is called the configuration work; it is an inexact differential, i.e. work is not a state variable.
The amount of work done changing the configuration of a system from one state to another depends on how the work is done, i.e. on the path taken between the final and initial states. The path must be specified in order to calculate work via integration.
I explained why configuration work is inexact on the previous slide.
Stress the convention that positive work is work done BY the system.

10. What do we mean by reversible?
Why is it an inexact differential?

11. Configuration Work
This is the work done in a reversible process given by the product of some intensive variable (y) and the change in some extensive variable (X). The most general case would be:

12. Dissipative Work Examples: Stirring Resistive electrical heating
This is the work done in an irreversible process; it is always done ‘on the system’.
Total work is the algebraic sum any configuration work and any dissipative work.
If a process is reversible, then dissipation is necessarily zero.
Examples: Stirring
Resistive electrical heating
Frictional work
Plastic deformation
Many chemical reactions
There are some simple examples here: work done by a battery attached to a resistor, i2R; does not matter which way the current flows, the battery always ends up doing positive work. Not surprisingly, this work is converted to heat energy in the resistor and lost irreversibly to the surroundings. Friction F dot v; when you reversse v, F reverses as well, so the sign of the work remains unchanged.

13. Microwave oven

14. Do not confuse between exact differentials and reversible processes.
Reversible processes need not be exact differentials.
Why is it called reversible then?