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Lecture 5
Physics 2016/2017
Thermal physics
Temperature – T (t) –
Intrinsic property –
independent on the
amount of the material
temperarure = average kinetic
energy of molecules
[T] = 1 K = 1oC
T = t + 273.15 oC
Measurement of temperature
properties of materials varying with temperature
• volume
• electrical properties
• pressure (gauges thermometers)
• IR radiation….
• Temperature scales
Kelvin – [T] = 1 K
Celsius – [t] = 1 oC
0 oC = 273.15 K
100 oC = 373.15 K
water freezing-boiling
T1 K = (t1 + 273.15 ) oC
T2 K = (t2 + 273.15 ) oC
(T1 - T2) K = (t2 - t2 ) oC
T=0K => p=0, V=0 impossible
to reach
• Thermal expansion of materials
α – linear (area, volume ) thermal expanson coefficient [α]=K-1
• Density variation with temperature
Density decreases with increasing temperature!
• Anomaly of water density
0<t<3.98oC β<0, the density increases with t
t=3.98oC
β=0, density has maximum
t> 3.98oC
β>0, density decreases with t
“normal” behaviour
• Thermodynamics – branch of physics
concerned with heat and temperature and
their relation to energy and work
Thermodynamic system is the content of a
macroscopic volume in space, along with its
walls and surroundings; it undergoes
thermodynamic processes according to the
principles of thermodynamics.
Thermodynamic systems –
•
•
•
•
open system – energy, matter exchange
closed system – energy, matter exchange
isolated system - energy, matter exchange
adiabatic process – no heat or matter
exchange, internal energy transfer to work
State functions - their values do not depend on
the path, done by the system to get to the
given state (internal energy, entropy...)
Process (path) functions – heat, work depend on
the path
intensive – independent on the number
particles, T, p, Vm…
extensive – dependent… V, n
but
Vm=V/n
molar volume – intensive
Vs=V/m
specific volume - intensive
State functions
ΔX12= -ΔX21
Path function
ΔXA= -ΔXB =- ΔXC
ΔX= ΔX1 +ΔX2 +ΔX3 +ΔX4
Exact differential (total differential)
example
Ideal gas
• the molecules are point-like particles
• elastic collisions
• no interactions between the particles, except
the collisions
Real gases behave similarly at high temperatures
and low densities
• molecules have non-zero volume
• interactions
• not allways elastic collisions
• Brownian motion
• Thermodynamic state – system fully identified
with a suitable set of state variables (function)
for examples: pressure p, volume V,
temperature T, number of moles n.
Gay-Lussac I. law, Charles’ law, Law of Volumes
isobaric process
State variables: V,p,T
p = const.
Pressure – temperature law, Gay-Lussac II.law
isochoric process
V= const.
Boyle-Mariotte law
isothermal process
T=const.
pV= const.
Avogadro’s law
Under the same conditions of temperature
and pressure, equal volumes of different
gases contain an equal number of molecules
(regardless on their chemical nature and
physical properties).
NA= 6.02214129 × 1023
Vm=22,41 dm-3=22,41 l
(T=273,15K,p= 101 325 Pa)
Avogadro’s number or Avogadro constant.
𝑉 = 𝑛 𝑉𝑚
p=101 325 Pa, T= 273.15 K
Vm = 22.41 L = 0.02241 m-3
NA=6.022x1023
Ideal gas law
Gay-Lussac laws
V= const . T
p= const . T
Boyle-Mariotte
pV = const
Avogadro
V = const . n
Ideal gas law
pV=n R T
R= 8.314 JK-1mol-1
k= R/NA = 1.3806 x 10-23 JK-1
pV=N kBT
N=nNA
universal gas constant
Boltzmann constant
kB–bridge from macroscopic
to microscopic physics
Dalton´s law – mixture of gases
𝑛=
𝑛𝑖
𝑖
𝑛𝑅𝑇
𝑝=
=
𝑉
𝑖
𝑛𝑖 𝑅𝑇
=
𝑉
𝑝𝑖
𝑖
In a mixture of non-reacting gases, the total pressure exerted
is equal to the sum of the partial pressures of the individual
gases.
𝑝𝑖 =
𝑛 𝑖 𝑅𝑇
𝑉
Each gas exerts the same pressure they would exert if they
were in the container alone.
Real gases
Real gases – particles not point mass, real volume
– not negligible interactions, attraction-repulsion,
non-elastic collisions.
van der Waals equation
𝑛2 𝑎
𝑝+ 2
𝑉
𝑛2𝑎
𝑉2
𝑉 − 𝑛𝑏 = 𝑛𝑅𝑇
- correction for non-elastic interactions, attraction-
repulsion
𝑛𝑏 – correction for the real volume of particles
a,b – material constants, determined experimentaly
• Heat and temperature
Q [Q] = 1 J (energy)
transfer of heat – change
of temperatures
c – heat capacity [c] = J K-1
cm – molar heat capacity [cm] = J mol-1K-1
cs – specific heat capacity [cs] = J kg-1K-1
• Work of ideal gases (W, A) [W] = 1J
W = -Fex Δx = -p S Δx = -p ΔV
Sign convention – from the point of view of the system
receives
releases
Q:
+
W=-∫pdV
+
ΔV<0 compression ΔV>0 expansion
Zeroth law of thermodynamics
If two bodies are each in thermal equilibrium
with some third body, then they are also in
equilibrium with each other.
Thermodynamic equilibrium (steady) state
equilibrium – stable, unstable, indifferent
Thermodynamic equilibrium, condition or state of a
thermodynamic system, the properties of which do not
change with time and that can be changed to another
condition only at the expense of effects on other
systems.
entropy (at given energy)- maximum,
Gibbs free energy (at given p, T) - minimum
Reversible process – is a process that can be "reversed" by
means of infinitesimal changes in some property of the
system. A reversible process does not increase entropy
of the system and surroundings. During a reversible
process, the system is in thermodynamic equilibrium
with its surroundings throughout the entire process.
Real processes are not reversible!
Summary
Thermal expansion
𝐿 = 𝐿0 (1 + 𝛼Δ𝑇)
Ideal gas law
𝑝𝑉 = 𝑛𝑅𝑇
van der Waals equation
𝑝−
𝑛 2𝑎
𝑉 = 𝑉0 (1 + 𝛽Δ𝑇)
𝑉 − 𝑛𝑏 = 𝑛𝑅𝑇
𝑉2
Avogadro’s law
𝑉 = 𝑛 𝑉𝑚
Heat
𝑄 = 𝑐𝑚 𝑛∆𝑇 = 𝑐𝑠 𝑚∆𝑇
Work (volume)
𝑑𝑊 = −𝑝𝑑𝑉
Dalton’s law
𝑝=
𝑖 𝑝𝑖 =
𝑖
𝑛 𝑖 𝑅𝑇
𝑉
𝜚 = 𝜚0 (1 − 𝛽Δ𝑇)