ENTROPY: S = rev Q/T (11.8) The novelist and physicist C. P. Snow once remarked that not knowing the 2nd Law of Thermodynamics was analogous to never having read a work by Shakespeare. 1st law of thermodynamics – cons. of energy – states that heat can be transformed into work, the second law concerns itself with how much. Like first law, based on experience The property associated with the capability of a system for spontaneous change is called its entropy. Name coined in 1850 by Clausius.

Laws of Thermodynamics 1854 ~ (Q1/T1)rev = (Q2/T2)rev 1850 ~ 1st & 2nd Laws of Thermodynamics 1854 ~ (Q1/T1)rev = (Q2/T2)rev 1865 ~ dS = dQ/Trev dS > dQ/Tirrev “I propose to name the magnitude S the entropy of the body, from The Greek word for transformation. I have intentionally formed the word entropy so as to be as similar as possible to the word energy, since both these quantities….are so nearly related…”

Definition of Entropy: S = revQ/T or dS = [Q/T]rev (11.8) Because of 2nd Law: dS  [Q/T]irrev or TdS  Q (11.9a)

IRREVERSIBLE AND REVERSIBLE PROCESSES A process is reversible if system remains in equilibrium, i.e. if the work and heat are added in such a way that there are no currents. A currents of heat arises from temperature gradients; a current of mass arises from concentration gradients; a current of momentum flows, if there are differences in velocity. Hence, reversible process will have no density, velocity and temperature gradients. All natural processes are irreversible, not in equilibrium, associated with currents.

It can be shown for ideal gas and reversible cycle isothermal It can be shown for ideal gas and reversible cycle That QH/TH = QC/TC so over a cycle there is no gain or loss of Q/T. Call Q/T the entropy, S. adiabatic isothermal adiabatic

dS  [Q/T]irrev or TdS  Q (11.9a) dS = [Q/T]rev (11.8) dS  [Q/T]irrev or TdS  Q (11.9a) Tds = Q/m = q (reversible/11.8) (11.9b) Tds  Q/m = q (irrev./11.8) (11.9c) ds = 0 (rev. & adiabatic/11.9b) (11.9d) ds > 0 (irrev. & adiabatic/11.9c) (11.9e) Isentropic if reversible and adiabatic Reversible if isentropic and adiabatic Adiabatic if reversible and isentropic

Q/m = Tds for reversible process Tds = du + pdv (11.10a) Energy Equation: Q/m - pdv = du Q/m = Tds for reversible process Tds = du + pdv (11.10a) Note: Although 11.10a was derived for a reversible processes, it is also valid for irrev. processes as it involves only exact differentials having integrated values that are independent of process.

Tds = du + pdv (11.10a) Definition: h = u + pv dh = du +(dp)v + p(dv) Tds = du + dh - du - (dp)v Tds = dh - v(dp) (11.10b) Note: Although 11.10b was derived for a reversible processes, it is also valid for irrev. Processes as it involves only exact differentials having integrated values that are independent of process

Timeline of steam: 150 BC-159 AD Hero James Watt (1736-1819) is fancifully depicted here as a boy entranced by the nature of steam. Timeline of steam: 150 BC-159 AD Hero 1600s Torricelli/Viviani – creation of vacuum 1650 von Guericke – invents air pump 1698 Savery – makes a steam pump 1712 Newcomen – better pump using condensing steam 1769 – Watt greatly improves Newcomen’s design 1804 – first stem driven rail road 1812 – first stem driven ship

For an ideal gas pvk = const For an ideal gas pv = RTH QH isothermal adiabatic isothermal QC adiabatic For an ideal gas pvk = const

Reversible Processes pv = k pv1.4 = k

Work = pdV (Watt’s Secret)