THE SECOND LAW AND ENTROPY

I. Reversible processes can help us understand real processes

II. A reversible process is a process after which the system and surroundings can be restored to their initial states with no changes elsewhere.

A. Approach reversibility by using infinitesimals

B. All natural processes are irreversible

1. Temperature gradients produce irreversibility

2. Friction also produces irreversibility

III. Carnot Cycle - a reversible cycle

A. A cycle consisting of two isothermal processes and two adiabatic processes - use an ideal monatomic gas in a frictionless cylinder/piston container

 PROCESS PATH Q E W ISOTHERMAL EXPANSION AT TH a TO b QH = nRTHln(Vb/Va) 0 Wab = nRTHln(Vb/Va) ADIABATIC EXPANSION b TO c 0 Ebc = (3/2)nR(TC-TH) Wbc = -(3/2)nR(TC-TH) ISOTHERMAL COMPRESS AT TC c TO d QC = nRTCln(Vd/Vc) 0 Wcd = nRTCln(Vd/Vc) ADIABATIC EXPANSION d TO a 0 Eda = (3/2)nR(TH-TC) Wda = -(3/2)nR(TH-TC)

B. Using the First Law, we find for the cycle that the change in internal energy for the gas is zero and that the work done per cycle is: W = QH - QC (Note: The Q's here are absolute values)

C. For any heat engine: efficiency = (Work done)/(Heat in)

Here, efficiency = W/QIN

1. For a Carnot cycle only, the efficiency = 1 - TC/TH because QH/QC = TH/TC

D. What is a Carnot cycle operating in reverse?

IV. The Second Law of Thermodynamics - It is impossible for any cyclical engine to produce no other effect than to convey heat continuously from one body to another at a higher temperature.

IV. Recall that the amount of heat energy transferred depends on the process.

A. A new thermodynamic function can be defined that depends only on the initial and final states of the system and is related to the heat transferred along any reversible path. This is the ENTROPY

dS = dQ/T

B. Another statement of the Second Law: A natural process that starts from one equilibrium state and ends in another will go in such a direction that causes the entropy of the system and surroundings to increase.

1. Natural processes (irreversible processes): dS>0

2. Reversible processes: dS = 0