Download - 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.
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)