HEAT - THERMODYNAMICS
Harry Varvoglis
University of Tübingen &
University of Thessaloniki
Historical introduction
• Heat: a phenomenon known from pre-historic
times.
• Thermodynamics: relation between heat and
other forms of energy.
• Initially a branch of Chemistry (for the
interpretation of the direction of reactions).
• Example: the synthesis of ammonia for
the productions of synthetic fertilizers
(high temperature & high pressure &
catalyst, Fritz Haber, Nobel Prize 1918).
Thermometers
• What is heat and what is temperature? A usual confusion,
even among scientists.
• Thermometers measure temperature.
• Lack of thermometers: cause of delay in the development
of this branch of Physics.
• Expansion of gases: Philon of Byzantium (3rd century BC)
and Hero of Alexandria (1st century AD).
• First thermometer ever built: Galileo.
• First (accurate) water thermometer: Jean Rey (1632).
• Mercury thermometers: only beginning of 18th century.
• Measurement of amounts of heat: through calorimetry,
ΔQ = C∙ΔT
Phlogiston: an imponderable fluid
• Phlogiston (Johann Joachim Becher, 1635-1682 &
Joseph Black, 1728-1700): descendent of the 4th
element of Aristotle (fire).
• Axiom: Phlogiston is contained in all materials that can
be oxidized: wood, coal, metals.
• Experimental test: Lavoisier found that oxides are
heavier than metals → has phlogiston negative mass?
• Story on Lavoisier and Marat.
• The theory was abandoned!
• Moral: Basic element of the Philosophy of Science: One
can only prove that a certain theory is wrong, but
never that it is correct!
Caloric fluid
• Lavoisier: caloric is a fluid whose quantity is constant throughout the
Universe and which transfers heat, by flowing from hot to cold
bodies.
• Success of caloric: heat flow in a solid (Fourier), propagation of sound
in the air (Laplace-Poisson), 2nd axiom of Thermodynamics (Carnot).
• Lavoisier made experiments to measure it.
– He used a closed glass vessel containing water, which was evaporated
and condensed continuously.
– He got positive results (the water was heavier, due to dissolved silicon
from the glass!)
• But Benjamin Thompson observed the production of heat during the
boring of a canon, in seemingly unlimited quantities.
• He proposed that heat is a form of energy and not a fluid.
• He was able to calculate the mechanical equivalent of heat; in
modern units: 1 cal = 5,5 J (correct value: 4,186 J)
Calculation of the MEH by B. Thompson
2.5 h x 1 hp = m x ΔT = 12 lt x 100 oC
Benjamin Thompson (1753-1814)
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Born in Massachusetts, then a British colony.
In 1772 married a wealthy widow, Sarah Rolfe, 14-years his senior.
Fought on the side of British army, in the Anglo-American war.
1776 fled to UK and became under-secretary of state.
Returned to the army but did not have time to fight, since the Anglo-American war
ended in 1783.
Left the army as Lieutenant-Colonel and was honored with a knighthood by King
George III.
1785 joined the Austrian army against the Turks.
Became a Secretary of war in Bavaria (under elector prince Maximilian); built
canons and Englischer Garten; named Count of the Holy Roman Empire, under the
title of Reichsgraf von Rumford (from the name of the American town of his wife’s
family!).
1795: return to England.
1799: foundation of the Royal Institution.
1804: moved to Paris and married Lavoisier’s widow (which he later divorced).
Beyond Thermodynamics
Coffee percolator
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Rumford Fireplace
Announcement of Rumford’s wedding in the “social column” of a London
newspaper: "Married; in Paris, Count Rumford to the widow of Lavoisier; by which
nuptial experiment he obtains a fortune of 8,000 pounds per annum - the most
effective of all the Rumfordizing projects for keeping a house warm.“
Noteworthy: The man who introduced caloric and the man who discarded it were
married to the same woman…
1st axiom of Thermodynamics:
Julius Robert Mayer (1814-1878)
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Doctor in a ship, bound to Indonesia, noticed red vain blood in a sailor.
He reasoned that oxygen consumption was low, due to the high ambient
temperature. He tried to do the calculations.
He was aware of the molar specific heat capacities, CP & CV , measured by
Delaroche & Bérard (1811).
Work produced during the expansion of 1 mol of gas (under normal conditions),
due to heating by 1 oC:
WΘ = R = CP – CV cal
In mechanical units: WM = p0∙ΔV J
But, due to the expansion,
V = V0(1 + aθ) cm3
in which case, for the increase of θ by 1 oC: ΔV = V0a
and, therefore, WM = p0∙ΔV = p0V0a J
He calculated the MEH without making any experiment!
WΘ = WM → 1 cal = 3.58 J (due to the inaccurate values of CP και CV)
James Prescott Joule (1818-1889)
• Brewer and amateur scientist.
• Similarity with Student
(William Sealy Gosset, of Guiness).
• Tried to construct a perpetual
motion machine with the aid
of a battery.
• He found, instead, the law Q = I2R.
• 1847: announced his first result on the MEH.
• 1875: after a request by the Royal Society, he
gave his best value, 4.15 J/cal (in modern units).
Experimental measurement of the
mechanical equivalent of heat
Original Joule’s equipment, 1845
Who was the first to formulate
the 1st Axiom of Thermodynamics?
• Joule and Helmholtz dismissed, initially, Mayer’s
idea on the nature of heat, because he was not a
professional scientist.
• Finally the former calculated the same physical
quantity with greater accuracy, while the latter
formulated mathematically the first axiom of
Thermodynamics (only in 1851!).
• Mayer was admitted in a mental health hospital,
after a suicide attempt. He got the due
recognition only in late age, when he was not
able to enjoy it.
2nd axiom of Thermodynamics:
Sadi Carnot (1796-1832)
• Carnot was the son of a Napoleon’s general
and a captain in the French army.
• He realized that the war with England had
an economic side, as well.
• How one can optimize the function of a thermal engine?
• He considered an analogy: the flow of heat vs. the flow of water in
a watermill.
• The flow of caloric should be smooth, without vortices.
• Therefore flow at very low speed → reversible.
• Carnot’s ideal thermal engine, private publication (1824).
• Analogies: falling water – moving caloric
• Watermills efficiency:
• Heat engine’s efficiency:
mghtop  mghbottom
mghtop
Thigh  T low
Thigh
2nd axiom of Thermodynamics:
W. Thomson
• Read about Carnot’s “ideal heat engine” in a book by Clapeyron (1833).
• Obtained finally a copy of Carnot’s booklet in 1841 or 1842.
• Proved that
Thigh  T low
Thigh
=
Qhot  Qcold
W

Qhot
Qhot
because, due to the fact that ΔQ = k∙ΔT,
Qhot
T
 hot
Qcold Tcold
• He understood that a “correct” scale of temperatures could not have
negative values, because if Tlow < 0, (Thigh  Tlow )  Thigh
and
Thigh  Tlow
Thigh
Therefore the efficiency of the heat engine would be greater that 1, in
which case the first axiom of Thermodynamics is violated!
1
William Thomson, the scientist
•Studied in Cambridge.
•Professor in the University of Glasgow for over 50 years
(declined the directorship of Cavendish Lab).
•The greatest physicist of his time. Not so today!
•One famously wrong result: Age of Earth through
cooling and solidification: 20-40 My, in disagreement
with biologists (Darwin) and geologists, who estimated
the age in Gy.
•Solution: heating of the young Earth by nuclear fission.
•Young age – studies: “programmed” to become a
professor.
•He accepted that heat is a form of energy only in 1851,
well after Joule’s experiments.
•The last one of the “classical” physicists.
•He was aware of the problems that were unsolved in
the dawn of the 20th century.
-Famous lecture: Nineteenth-Century Clouds over
the Dynamical Theory of Heat and Light
William Thomson, the engineer
• W. Thompson was a consultant of the company
deploying a transatlantic telegraph cable.
• He understood that the signal travels with a finite
speed, and wrote a PDE for this (the chief engineer had
a different opinion).
• The facts showed that Thomson was right. He was
admitted in the governing council of the company, with
a good salary.
• He was put on charge of the operations.
• After the successful deployment of two cables, he was
knighted by the Queen (Kelvin is the name of a small
river, near his house in Scotland).
William Thomson, the yachtsman
• His first wife died in 1870.
• The same year he bought a 126-ton schooner, the Lalla Rookh (from
on oriental romance by Thomas Moore).
• In 1873, onboard a cable-deploying ship, spent a 16-day stopover in
Madeira.
• He spent some time with the Blandys, an English family having
three daughters.
• Next year he sailed to Madeira with Lalla Rookh and, upon entering
the harbor, signaled to the Blandy’s residence: “will you marry
me”?
• Fanny, the eldest daughter, signaled back: “Yes”.
• They were married next year.
• The story sounds very romantic to me.
• But it should be noted that he was 50 and she was 37.
Entropy: Rudolph Clausius (1822-1888)
• 1st axiom of TD: dQ = dU + dW = dU + pdV
• 2nd axiom of TD: definition of entropy, through the
relation dS = dQ/T (1865)
• For a closed and reversible cycle
B
dQ
• In general S A  S B  
T
A

dQ
0
T
• Corolary: Entropy never decreases in a closed system.
Entropy - II
• Entropy: a physical quantity that shares some of the properties of
mechanical energy in a conservative field (it is a perfect differential).
• If there is no friction, then a body returns to the same point with the same
mechanical energy.
• Correspondence between:
– entropy - reversibility and
– friction - energy conservation
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Cosmological consequences:
– Same temperature (not necessarily zero!)
– No heat transfer -> no work produced
• One should take into account the nature of gravitational forces (longrange), the expansion of the Universe and its finiteness or infiniteness (we
can extract “infinite” energy from a simple 3-body point-mass gravitational
system!).
• The expansion leads to weaker and weaker gravitational forces, but maybe
increases the value of the “final” entropy faster than the value of the actual
entropy increases.
• Thermodynamics and Entropy are “expanded” to include General Relativity
and, even, in some cases they may act as a “connection” between GR and
Quantum Mechanics.
Thermodynamics today
• Today Thermodynamics is taught in the form (axioms etc.)
established by Gibbs (Josiah Willard Gibbs, 1839-1903), the first
“professional” American scientist.
• Note that there exists different axiomatic foundations (e.g.
Caratheodory’s does not use heat as an axiomatically introduced
concept!)
• Thermodynamics is the “singular” point of Physics.
• The axioms, on which it is founded, are different from the axioms of
all other chapters-disciplines of Physics.
• Yet it acts as the “butter” in a sandwich, interconnecting the other
chapters together (e.g. the “quantization” of Gravitation by
Hawking).
• Black hole, black-body radiation: temperature of a black hole,
dS = dQ/T .
• Generalized Entropy in GR: inclusion of the black holes’ area.
• Modern Thermodynamics: direct relation to the theory of (perfect)
gases.