The Thermodynamic Processes
The Foundation Course on Physics
Professor Vojtěch Mornstein
Glencoe pp. 318 – 355, 368-371
Back to Ideal Gas Law
• Ideal gas law:
• The state parameters (quantities which values determine/describe a
thermodynamic state) are interrelated by the state equations.
• The simplest state equation: the ideal gas law (= state equation of ideal
gas), which can be written in different ways e.g.:
pV = nRT
(for constant amount of substance n – this value becomes a component of the constant) ,
• where p is the gas pressure given in [Pa], V is the volume of the gas [m3], T
is the Kelvin temperature* [K], R the molar or universal gas constant (=
8.32 J·K-1·mol-1), and n is amount of substance in moles [mol].
*Kelvin temperature = absolute temperature = thermodynamic temperature
2
22
1
11
.
T
Vp
T
Vp
const
T
pV
nR
T
pV
===
Normal values of p and T
• For many calculations in thermodynamics, it is necessary to know what
are the values of normal molar volume Vn, normal pressure pn and normal
temperature Tn:
• pn = 1.01325×105 Pa = 101,325 kPa = 1013,25 hPa ≈ 1 atm
• Tn = 273.15 K* (0 °C)
• Vn = 22.4×10-3 m3mol-1 = 22.4 litres
• (Note: All gases have the same molar volume at the same temperature
and pressure!!!!!)
Normal molar volume is a volume occupied by one mole of perfect gas at
normal pressure pn and temperature Tn. Based on the equation of ideal gas
law, it is possible to derive** simply other laws which are applicable only
under some specific conditions. Processes described by these laws are
reversible and can be presented as curves of a typical shape in a pVdiagram
(Fig.).
*It can be also 293.15 K, but it will influence the molar volume too.
**The historical development was different!
Thermodynamic processes
a) Boyle's law (Boyle – Mariotte law):
During an isothermal process, temperature T has a constant value (does not
change). Value of temperature is included in the constant below.
p1V1 = p2V2 = const.
A gas is slowly compressed (or
expanded) and the heat can be
transferred to/from the
surrounding: slowly inflating a
rubber balloon, bubbles
ascending in water …..
In homoeothermic organisms
most processes take place at
constant temperature!
.... constconstTpVconst
T
pV
===
Thermodynamic processes
• b) Gay-Lussac's law:
• Pressure p is constant – an isobaric process takes
place. Value of pressure is included in the constant:
.
2
2
1
1
const
T
V
T
V
== The weight
exerts always
the same force
on the gas
under the
movable piston.
Volume and
temperature
are changing
but pressure is
constant
A gas is slowly heated and its
volume increases at a constant
pressure: most processes
around us take place under
constant pressure…
like in the most living
organisms!!!
Thermodynamic processes
• c) Charles's law:
Volume V is constant – an isochoric (i.e. isosteric)
process takes place. Value of volume is included in
the constant:
.
2
2
1
1
const
T
p
T
p
==
A system consisting of water
and water vapour is slowly
heated and its volume is kept
constant: cooking in a pressure
cooker ….. autoclave used for
sterilization in labs is similar.
The piston
does not
move,
pressure and
temperature
increases.
Pressure cooker and Autoclave
kitchen
Small lab
industry
Thermodynamic processes
(optional)
• A special case – adiabatic process. The system is
thermally insulated. In the following equation the k
(kappa) is the Poisson constant which has different
values for different gases.
pVk = const.
In real conditions, adiabaticlike
processes are fast enough
to avoid heat exchange with
surroundings.
Only internal
energy U can be
transformed into
useful work W!
Thermal
insulation
p-V diagram
The pV-diagram is the most often used graphic representation of the
reversible thermodynamic processes (see also the slide about the
isothermal process!). What is the meaning of any single point in a p-V
diagram? For an ideal gas and n = const., this point represents a single
thermodynamic state!
A reversible
TMD process
can be
represented by
a line (point by
point = state by
state) !!!
For example:
pV - diagram
• Different thermodynamic processes are represented by
different shapes of p(V) function – it means they have
different pV-diagrams.
• 1 – isothermal,
The line is an isotherm
• 2 – isobaric,
The line is an isobar
• 3 – isochoric*
The line is an isochore
• 4 – adiabatic (also isoentropic**).
The line is an adiabat
*called also isovolumetric or isosteric **entropy – see next lecture
Thermodynamic systems can do some
work!
Work done in TMD processes
• 1 – isothermal
• 2 – isobaric
• 3 – isochoric
• 4 – adiabatic
process
1
2
ln
V
V
nRTW =
VpW =
)0(0 == VW
1
2211
−
−
=
k
VpVp
W
Work done is
always equal to
the area below
the p(V) curve!
It can be seen
best in case of
isobaric
process.
Heat and Heat Capacity
We know already: Heat energy Q is the energy related to thermal
motion of molecules*. It is interchanged between thermodynamic
systems during thermodynamic processes. The thermal motion is
chaotic movement of particles which move accidentally in all
possible directions.
Vector sum of vectors of their velocities would be equal to zero (which
is not so when we summarise or average absolute values of particle
velocities or their second powers).
The unit of heat energy is joule [J]. An often used old unit of heat, the
calorie** (amount of the heat necessary for heating 1 g of water by
1 oC) is:
1 cal (calorie) = 4.186 J
British thermal unit 1 BTU = 1 055,05585 J (In Czechia, BTU is
almost unknown)
*Heat can be interchanged also in the form of radiation
**Calories used for description of energetic content of the food are the so-called big
calories (kilocalories)
Heat and Heat Capacity
Heat capacity. Heat interchange can cause a change of body temperature. Heat capacity K
of a body is the amount of heat causing a temperature increase of 1 oC. We can write:
Q = K·ΔT
Specific heat capacity C is the heat capacity of unit mass of a substance:
Q = C·m·ΔT,
where C is given in [Jkg-1K-1], m is mass of substance [kg], ΔT is the temperature change [K],
and Q – heat interchanged [J].
C depends on the kind of thermodynamic process.
Cp – heat capacity measured in an isobaric process (at constant pressure) – is greater than
Cv – heat capacity measured in an isochoric process (at constant volume).
In the first case it can be explained by doing work, which consumed a part of absorbed
heat. In the second case (Cv) no work can be done because the “piston” cannot move
(V = 0).
T
Q
K

=
Tm
Q
C

=
Some specific heat capacities
Huge amount of heat can be stored in the seas – it
stabilises temperature of Earth surface!!!!!
Calorimetry
The „system“
interchanges
heat with the
water bath:
Qw = QS mwCw(Tf – Tw) = mSCS(TS – Tf),
Where mw is mass of water, Cw is specific heat capacity of water, Tf is final
temperature of water+system, Tw is initial temperature of water, mS is mass of
the „system“, CS is specific heat capacity of the „system“, TS is initial
temperature of the „system“ .
To obtain correct results of calculations we have to consider also the heat
capacity of the calorimeter itself!
Thermal conductivity
• Equation of thermal conduction. A steady heat conduction can be
easily illustrated by a rod (cylinder) of a length d one end of which is
kept at the temperature t1 and the second one at the temperature t2.
The temperature difference t = t2 - t1 is constant, the temperature
decreases uniformly from the warmer end to the colder one. The
fraction t/d denotes the temperature gradient. Amount of heat Q
which passes through the rod in an arbitrary (normally oriented) crosssection
A during time t is:
• The proportionality constant l is the coefficient of thermal
conductivity. By the magnitude of this coefficient we can distinguish
good and poor thermal conductors – the second ones are called thermal
insulators. Water belongs among relatively good heat conductors, even
better are the metals. Typical thermal insulators are e.g. glass, plastics,
porous materials, feathers, textile, glass wool etc.
tl
d
tt
AQ 12 −
=
Thermal conductivity
Heat flux in a metallic rod. Is it (could it be) a steady flux?
Discuss the problem. Consider the ambient medium.
Thermal conductivity
• The above equation of heat conduction is the simplest
mathematical representation of the problem which
otherwise has to be solved by means of integration of
differential equations.
• Thermal resistance R characterises thermally insulating
properties of a material layer of given thickness. If we know
the value of the coefficient of thermal conductivity of the
material layer, and the heat is transmitted uniformly and
normally to the material layer, the thermal resistance is
defined as
R = d/l,
where d is the layer thickness [m] and λ [W·m-1·K-1] is the
coefficient of thermal conductivity.
Thermal conductivity
There are some differences / how to
explain them?
How to explain apparent difference
between the diamond and the air?
Thermal expansion of liquids and solids
Thermal expansion:
Changes in temperature lead to expansion or contraction of solids and
liquids. In most cases, the dimensions of a body increase with
temperature. Thermal linear expansion will be explained first:
Δl = αl0ΔT i.e. l = l0 + αl0ΔT [m],
where Δl = l – l0 is the linear (longitudinal) expansion [m], ΔT is the
temperature increase [K or oC], l0 is the initial length of the body,
and α is the coefficient of linear expansion (called also linear
thermal expansivity).
Thermal expansion of liquids and solids
Thermal volume expansion can be expressed in the following way:
ΔV = bV0ΔT i.e. V = V0 + bV0ΔT
b is coefficient of volume expansion. It can be approximated: V ≈ V0 + 3αV0ΔT (b ≈ 3a)
Material a coefficient
[°C-1]
l per 1 m and
T 100 °C
b coefficient
[°C-1]
V per 1 litre
and T 100 °C
aluminium 2310-6 2.3 mm 6910-6 6,9 ml
Bottle glass 910-6 0.9 mm 2710-6 2,7 ml
Cooking glas 310-6 0.3 mm 910-6 0,9 ml
Concrete 1210-6 1.2 mm 3610-6 3,6 ml
copper 1710-6 1.7 mm 5110-6 5,1 ml
methanol ----------- --------- 120010-6 120 ml
gasoline ----------- --------- 95010-6 95 ml
water ----------- --------- 21010-6 21 ml
Thermal expansion of liquids and solids
• Applications and examples:
It can happen in
very hot days!
Thermal expansion of liquids and solids
Expansion loops and
joints
The end
Version 2020