Thermodynamics is the study of the relationships between heat and
other forms of energy. It is based on Kinetic Theory, which assumes
that (i) all matter is composed of tiny particles (atoms or molecules),
and (ii) these particles are in constant motion. Here are some of the
things you must know.
1. Since heat is a form of energy, it is measured in Joules but can also
be measured in kilocalories (kcal) with the conversion factor being
1 kcal = 4186 Joules.
2. The Celsius and Kelvin temperature scales are widely used in
scientific work. One Kelvin is equal to one degree Celsius, and
ΔTK = ΔTC. To change a Celsius temperature to Kelvin use,
TK = TC + 273.15.
3. The Kelvin (K), is named after William Thomson, Lord Kelvin (1824-
1907), British. The Celsius scale was devised by the Swedish astronomer
Anders Celsius (1704-1744) and was based on the properties of water.
4. At absolute zero, 0.0 K, or -273.15 C, matter has a minimum thermal
energy. This is regarded as the lowest temperature attainable.
5. Most solids expand when heated and contract when cooled. To
measure this this effect linearly, we use the equation ΔL = α·Lo·ΔT ,
where α is the coefficient of linear expansion.
6. For volume expansion, we use the equation ΔV = β·Vo·ΔT ,
where β is the coefficient of volume expansion.
7. In an isolated system, a quantity of heat, Q , can be exchanged
between substances but the total energy of the system is constant.
This is known as the Law of Heat Exchange, QL = QG .
8. The quantity of heat gained or lost by any material can be calculated
using the equation, Q = m·c·(Tf -Ti) , with m = mass, c = specific heat
capacity, and (Tf -Ti) being the temperature change, ΔT.
9. The equation for phase-changing processes is Q = mL.
10. Relative humidity is defined as a percent, based on the ratio
(Partial pressure of water vapor)/(Equilibrium vapor pressure of
water at the existing temperature) x 100 . The Dew Point is the
temperature below which the water vapor in the air condenses.
11. The conduction of heat through a bar of length L can be measured
with the equation, Q = (k·A·ΔT)t/L , with k being the thermal
conductivity, A is the cross-sectional area, T the change in temperature,
and t being the time.
12. The radiant energy, Q, emitted during a time, t, by an object whose
surface area is A, and whose Kelvin temperature is T, is given by the
Stefan-Boltzmann Law of Radiation, Q = e·σ·T4·A·t .
13. The constant, σ = 5.67x10-8 J/(s·m2·K4) , is known as the Stefan-
Boltzmann constant, and e is the emissivity, a dimensionless number
characterizing the surface of the material. The emissivity lies between
0 and 1, with 0 for a non-emitting surface, and 1 for a perfect blackbody.
14. The net radiant power is the power an object emits minus the power
that it absorbs. The net radiant power emitted by an object of
temperature T located in an environment of temperature To, is given by
the equation, Pnet = e·σ·A(T4 - To4).
15. The number of moles n contained in a sample is equal to the number of
particles N (atoms or molecules) in the sample divided by the number of
particles per mole NA. We then have the equation n = N/NA, where
NA = 6.022x1023 particles per mole, known as Avogadro’s Number, from
Amedeo Avogadro (1776-1856), Turin, Italy.
16. The number of moles is also equal to the mass m of the sample (expressed
in grams) divided by the mass per mole (expressed in grams per mole ). This
gives us the equation n = m/(mass per mole). The mass per mole (in g/mol)
of a substance has the same numerical value as the atomic or molecular mass
of one of its particles (in atomic mass units).
17. The mass of a particle (in grams) can be obtained by dividing the mass per
mole (in g/mol) by Avogadro's number: mparticle = mass per mole/NA.
18. The ideal gas law relates the absolute pressure P, the volume V, the number
n of moles, and the Kelvin temperature T of an ideal gas, or PV = nRT, here
we have R = 8.31 J/(mol∙K), the universal gas constant. An ideal gas is one
that within a range of densities, temperature, volume, and pressure have a
19. An alternative form of the ideal gas law is PV = NkT, where N is the number
of particles and k = R/NA = 1.38x10-23 J/K , a constant named after Ludwig
Boltzmann (1844-1906), Austria, who developed the branch of Physics known
as Statistical Mechanics.
20. When a gas is kept at constant temperature, its pressure is inversely
proportional to the volume. This is Boyle's Law PiVi = PfVf , named after Robert
Boyle (1627-1691) from Ireland.
21. Also, when the pressure is kept constant, the volume is directly proportional
to the temperature. This is the law of Charles and Guy-Lussac Vi/Ti = Vf/Tf ,
by Jacques Charles (1746-1823) and Joseph Louis Guy-Lussac (1778-1850),
both from France.
22. The equation that applies here is KEavg = ½ mv2rms = 3/2 kT, where
vrms is the root-mean-square speed of the particles, derived statistically.
The internal energy U of n moles of a monatomic ideal gas is U = 3/2 nRT.
23. Diffusion is the process by which solute molecules move through a solvent
from an area of higher concentration to an area of lower concentration. Fick’s
Law, named after Adolf Eugen Fick (1829-1901), Germany, states that the
mass of a solute that diffuses in time through a channel of known length and
cross-sectional area is given by m = (D·A·ΔC)t/L . In this equation, ΔC is the
solute concentration difference between the ends of the channel, and D is the
24. Thermodynamics is the study of heat and how it relates to the other forms
of energy (mechanical, light, sound, electric, magnetic, atomic, and nuclear).
The Zeroth Law of Thermodynamics states that two systems are in thermal
equilibrium if there is no net heat flow between them when they are brought
into thermal contact.
25. The First Law of Thermodynamics states that the total increase in thermal
energy of a system is equal to the sum of the heat added to it and the work
done on it, which is given by the equation ΔU = (Uf -Ui) = Q-W.
26. A thermal process is considered quasi-static when it occurs slowly enough
that a uniform pressure and temperature exist throughout the system at all
times. The work done in any kind of quasi-static process is given by the area
under the pressure versus volume graph.
27. An isobaric process is one that occurs at constant pressure. The work done
when a system changes at constant pressure from initial to final volume is
given by the equation W = P·ΔV = P(Vf -Vi).
28. An isochoric process is done at constant volume and no work is done. An
isothermal process is done at constant temperature. An adiabatic process
takes place without the transfer of heat.
18. When n moles of an ideal gas change quasi-statically from an initial to a
final volume at a constant Kelvin temperature, the work done is given by
W = nRT·ln(Vf /Vi).
29. When n moles of an ideal gas change quasi-statically and adiabatically
from an initial to a final Kelvin temperature, the work done is according to
W = 3/2 nR(Ti -Tf).
30. During an adiabatic process, and in addition to the Ideal Gas Law, an
ideal gas obeys the relation PiViγ = PfVfγ, where γ = cp/cv, which is the ratio
of specific heat capacities at constant pressure and constant volume.
31. The molar specific heat capacity of a substance determines how much
heat is added or removed when the temperature of n moles of the substance
changes. This is given by the equation Q = C·n·ΔT.
32. For a monatomic ideal gas, the molar specific heat capacities at
constant pressure and constant volume are, respectively, CP = 5/2 R and
CV = 3/2 R, where R is the Ideal Gas Constant equal to 8.31 J/(mol·K).
33. For any type of an ideal gas, the difference between CP and CV is R,
or CP - CV = R.
34. There are many equivalent statements for the Second Law of
Thermodynamics. In terms of heat flow, the second law declares that heat
flows spontaneously from a substance at higher temperature to a substance
at lower temperature.
35. The second law also states that natural processes always go in a
direction that increases the entropy, S, unavailable energy, or disorder, of a
system. ΔS = Q – W.
36. A heat engine continuously converts thermal energy to mechanical energy
and does work. The efficiency, e, of a heat engine is expressed by the
equation e = (Work done)/(Input heat) = W/QH.
37. Conservation of energy requires that the input heat of magnitude QH
must be equal to the work done plus the heat of magnitude QC rejected or
expelled to a cold reservoir. This gives us QH = W + QC. By combining the
previous two equations we arrive at the result, e = 1 – (QC / QH ).
38. A reversible process is one in which the both system and its
environment can be returned to exactly the same states they were in
before the process occurred. An alternate statement for the second law
was stated by French engineer, Sadi Carnot (1796-1832).
39. Carnot’s principle states that no irreversible engine operating between
two reservoirs at constant temperature can have a greater efficiency than a
reversible engine operating between the same temperatures. Furthermore,
all reversible engines operating between the same temperatures have the
40. A Carnot engine is a reversible engine in which all input heat QH
originates from a hot reservoir at a single Kelvin temperature, and all rejected
heat QC goes into a cold reservoir also at a single Kelvin temperature. For the
Carnot engine, we have QC/QH = TC/TH.
41. This gives an equation for the maximum efficiency that an engine can have
operating between two fixed temperatures. e Carnot = 1 - TC/TH.
42. A heat pump, air conditioner, or refrigerator uses mechanical energy to
transfer heat from an area of lower to higher temperature. These are governed
by the Law of Conservation of Energy with QH = W + QC.
43. The coefficient of performance of a refrigerator or air conditioner is given
by the equation Coefficient of performance = QC /W. For the heat pump
we have a similar relationship, Coefficient of performance = QH/W.
44. The change in entropy, ΔS, for a process in which heat enters or leaves a
system reversibly at a constant Kelvin temperature is ΔS = (Q/T)R, where
the subscript R stands for "reversible."
45. In terms of entropy, the second law states that the total entropy of the
universe does not change when a reversible process occurs
(ΔSuniverse = 0 J/K), and increases when an irreversible process occurs
(ΔS > 0 J/K).
46. Irreversible processes cause energy to be made unavailable for the
performance of work. This energy is given by Wunavailable = To·ΔSuniverse
where ΔSuniverse is the total entropy change in the universe and To is the
Kelvin temperature of the coldest reservoir into which heat can be rejected.
47. And still, we need these steps to solve any problem in Physics:
(i) read the problem and identify the given variables
(ii) determine what you are asked to solve for
(iii) find the correct equation to use
(iv) use Algebra, Trigonometry, and/or Calculus to isolate the unknown
(v) substitute-in the given information and simplify.
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End of Introduction to Thermodynamics. Click HERE to continue.
For a Sample Problem Set #1 on Thermodynamics. Click HERE.
For a Sample Problem Set #2 on Thermodynamics. Click HERE.
For REVIEW Problem Set on Thermodynamics. Click HERE.
For the Heat of Fusion Lab Handout. Click HERE.
For the Lab Abstract template. Click HERE.