2nd Law of Thermodynamics 1st Law: energy is conserved But is that enough ? –Object drops converting KE to heat but never see the opposite –H 2 and O 2 react to form H 2 O when ignited at room temperature but not the reverse 1st Law would permit the reverse but 2nd Law does not.

Irreversibility A flywheel is spinning in a fluid in an isolated box. Eventually flywheel (and gas) slow down and stop; the fluid is now hotter. KE flywheel has been converted to U fluid Organized motion has become random Reverse does not happen by itself

Entropy Mechanical energy [organized] generally more useful than heat [random]; i.e., it’s more valuable form of energy (e.g., flywheel can drive a generator directly). Entropy (S) is a measure of the disorder/randomness of a system. Systems naturally tend towards disorder.

Properties of the Entropy Entropy increases with increases disorder, reduced “useful” energy. Entropy can only be created not destroyed. (2nd Law) Production: P s =  S Isolated system P s =  S

Isolated System Can imagine 3 types of processes: P s < 0 impossible (2nd Law) P s = 0 reversible process; energy flow between thermal, mechanical, etc reversible. P s > 0 irreversible; to reverse need S to decrease - not in isolated system

Non-Isolated System Two types of reversible flow possible: Internally reversible, system always proceeds through equilibrium states with no entropy production Totally reversible: no entropy production in both system and surroundings Reversible processes are idealizations.

Entropy Transfer Rigid walled cylinder containing H 2 O At t 1 mostly ice, at t 2 mostly liquid Liquid more random S2 > S1 Where does the entropy come from ? Process is “reversible”; overall Ps for water = 0; how is entropy reduced during freezing ?

Entropy Transfer Heat transfer can lead to entropy transfer. As T increases in colder system, its randomness increases and vice versa. Work represents “organized” energy Work does not “transfer” entropy unless it is done irreversibly.

2nd Law for Closed System Two approaches for developing mathematical formulation: Postulate existence of entropy and relate to temperature [Reynolds & Perkins, Engineering Thermodynamics, McGraw Hill] Observe behavior of devices (cycles) and develop the concept of temperature [Black and Hartley, Thermodynamics, HarperCollins]

Deriving the 2nd Law (2nd approach) Postulate existence of S, describing microscopic disorder or amount of “useful” energy of a system. Systems A & B enclosed by rigid walls in contact; heat transfer ( ) only Combined system C is isolated

Equilibrium at Maximum Entropy Total energy, U c, fixed S C,final - S C,initial = P s ≥0 Let A & B not be in equilibrium S C = S A (U A,V A ) +S B (U B,V B ) Also: U C = U A + U B =  U C + (1-  )U C where  is the fraction of U C located in A S C increases until equilibrium is reached U 2 = U B U C = U A

T.D. Definition of Temperature S C = S A + S B, S=S(U,V, ), V constant =0 (equilibrium; i.e., T A = T B ) when

T.D. Definition of Temperature From above let: Show that above definition consistent with old idea that U increases with T

T.D. Definition of Temperature If T B > T A then 2nd Law: says dS c > 0, therefore d  > 0 Energy from B to A If is a maximum then

Some fancy math….

Does this agree with Traditional Idea of Temperature ?