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.

ENTROPY: S = rev Q/T (11.8)

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, sinceboth these quantities….are so nearly related…”

Definition of Entropy:S = revQ/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 momentumflows, if there are differences in velocity. Hence, reversible processwill have no density, velocity and temperature gradients.

All natural processes are irreversible, not in equilibrium, associatedwith currents.

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.

isothermal

isothermal

adiabatic

adiabatic

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 adiabaticReversible if isentropic and adiabaticAdiabatic if reversible and isentropic

Energy Equation:Q/m - pdv = duQ/m = Tds for reversible processTds = du + pdv (11.10a)

Note: Although 11.10a was derived for areversible 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 + pvdh = du +(dp)v + p(dv)Tds = du + dh - du - (dp)v Tds = dh - v(dp) (11.10b)

Note: Although 11.10b was derived for areversible processes, it is also valid for irrev. Processes as it involves only exact differentials having integrated values that are independent of process

James Watt (1736-1819) is fancifully depicted here as a boy entranced by the nature of steam.

Timeline of steam:150 BC-159 AD Hero1600s Torricelli/Viviani – creation of vacuum1650 von Guericke – invents air pump1698 Savery – makes a steam pump1712 Newcomen – better pump using

condensing steam

1769 – Watt greatly improves Newcomen’s design

1804 – first stem driven rail road1812 – first stem driven ship

isothermal

isothermal

adiabatic

adiabatic

For an ideal gas pv = RTH

For an ideal gas pvk = const

QH

QC

pv = k

pv1.4 = k

Reversible Processes

Work = pdV(Watt’s Secret)