1. Laws of Thermodynamics
Lecture 1
Laws of Thermodynamics
Thermodynamic state - equilibrium
Thermodynamic processes
Laws of thermodynamics
Absolute Temperature
Problems 2.5, 2.6, 2.8

2. Thermodynamic state - equilibrium
Thermodynamic intensive coordinates are uniform across the whole system (T, P, ) or across each macroscopic phase (e.g., water and ice density density at the melting point.
All thermodynamic coordinates are time independent
Mechanical equilibrium, thermal equilibrium and chemical equilibrium

3. Macroscopic vs. microscopic state
Thermodynamic coordinates (T, P, ) define macroscopic state of equilibrium.
Microscopic state is defined by atomic positions, and momenta - many microscopic states are consistent with a macroscopic state
Statistical mechanics connects microscopic description and detail with macroscopic state via ensemble average

4. Thermodynamic process  change of the thermodynamic state
Infinitesimal process  infinitesimal change of coordinates, e.g., dT, dV, dP
Quasi static process  always near equilibrium
Adiabatic process  no heat
Reversible process  can be restored to the initial state without charging surroundings

5. 0th law of thermodynamics
Two or more systems in equilibrium do not exhibit heat flow among each other, they are at the same temperature
Later we will see that criterion of equilibrium for isolated system, i.e., const E, V, T is the maximum entropy state
dS(E, V, N) = 0
dS = dS1+dS2 = 0
Allowing only energy exchange between two isolated systems
E1, V1, N1
E2, V2, N2
From conservation of energy

6. 1st law of thermodynamics - conservation of energy
dE = dQ-dW
d indicates inexact differential - depends on the integration path
In a cycle, E = 0
net Q in = net W out
Work and heat are not state functions
Energy is a state function
dW = Fdx can be PdV, -dl, -it

7. 2nd law of thermodynamics - entropy
For a reversible process
dQ= TdS
Where S is entropy which a state function, and T is an absolute temperature
The entropy can by calculated by integrating heat over a reversible path

8. Absolute temperature Consider the Carnot cycle
Since entropy is the state function Q1 T S T1 T2 Q2
Using reference T3 = K
Q > 0

9. Problem 2.5
When a system is taken from a to b state along abc 80 joules of heat flows into the system and the system does 30 joules of work.
How much heat flows into the system along path adb, if the work done by the systems is 10 joules.
When the system is returned from b to a along the curved path the work done on the system is 20 joules. Does the system absorb or liberate the heat? How much?
If Ea = 0 and Ed = 40 joules, find the heat absorbed in process ad and db. c b P V
Answers:
Qadb = 60 joules.
Qba = - 70 joules joules (liberate heat) of the heat
Qad= 50 J, Qdb= 10 J a d

10. Problem 2.6
A vessel of volume VB contains n moles of gas at high pressure. Connected to the vessel is a capillary tube trough which the gas may slowly leak out into the atmosphere, where P=P0. Surrounding the vessel and capillary is a water bath, in which is immersed an electric resistor. The gas is allowed to leak slowly trough the capillary into the atmosphere while, at the same time, electrical energy is dissipated in the resistor at such a rate that the temperature of the gas, the vessel, the capillary and the water is kept equal to that of the surrounding air. Show that, after as much gas is leaked as is possible during time , the change of internal energy is
where, v0 = molar volume of gas at P=P0,  = potential on the resistor, and i is the current.

11. Problem 2.8
The tension force in a wire is increased quasi statically and isothermally from 1 to 2. If the length, cross-sectional area and isothermal Young’s modulus (Y) remain practically constant, show that the work done by the wire is: