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Thermal Physics
Thermodynamics is the science that describes how
systems alter when their energy content changes
What do we already know?
• Conduction: atoms of a solid vibrate with increasing amplitude as
temperature increases
• Energy of atoms increases, internal energy of system increases
• Energy travels through vibrations
• Convection: movement of internal energy through a fluid
• Kinetic energy of particles increases as temperature increases
• Heating fluid causes it to expand and become less dense
• Less dense fluid rises to the top and more dense fluid falls
• Radiation: all objects emit and reflect electromagnetic radiation
• Increase temperature, range of frequencies and quantity of radiation
increases
• Black Bodies: Absorbs all thermal radiation at all wavelengths
• Reflects none of radiation
• As temperature increases:
• The amount of radiation from a black body increases
• Wavelength of peak emission falls (wien’s displacement law)
Heating up objects
• The Celsius scale is derived from the Kelvin scale:
t (℃) = T (K) – 273 K
• What do we see? Some objects need more energy than others to
raise their temperature by the same amount- it takes more energy
to heat water than the same mass of copper
• Why? Water molecules require more energy in order to move
around fast enough to increase temperature by 1 K
• The heat capacity is the amount of energy required to raise an
objects temperature by one kelvin.
• Unit = kJ K-1
• The specific heat capacity refers to the unit mass of a substance
∆𝑄
𝑐=
𝑚∆𝑇
Worked example
• A 3 kW kettle is used to bring 1.5 kg of water to the boil from a
starting temperature of 18 ℃. If all energy goes in to heating water,
what is the amount of energy and time required to boil the water?
c=4.20 kJ kg-1 K-1
• Energy = mc ΔT = 4.2 × 1.5 × 82 = 517 kJ
•
•
'()*+,
Power = -./)
'()*+,
345 78
Time = 012) = 9 78 :;<=
172 s
State changes
• When a substance goes from solid to liquid there is a latent heat
required to change the energy
• Latent heat does not cause any change in temperature
• We assume no energy is lost to the surroundings
• l = specific latent heat
• 𝑄 = 𝑚𝑙
Gas Laws
• Zeroth Law: If two bodies are in thermal equilibrium with a third
body, then they must be in thermal equilibrium with each other
• First Law: The increase in internal energy of a system is the sum of
the work done on the system and energy supplied thermally to a
system
• Second Law: It is not possible to have a thermal transfer of energy
from a colder to a hotter body without doing any work.
• Third Law: The entropy of a system approaches a constant value
as the temperature approaches zero.
First Law
∆𝑈 = ∆𝑄 + ∆𝑊
∆𝑊= the work done on a system.
∆𝑄 = thermal energy supplied to system
∆𝑈= increase in internal energy of a system
• Combinations of thermal energy and mechanical energy (work)
will cause changes in internal energy.
• Energy is transformed in many different ways, but it is not possible
to create or destroy energy.
Ideal gases
• Molecules move around inside cylinder, colliding
with walls and rebounding elastically
• Molecules change momentum as they collide off
walls
• Each molecule = small force on walls during a
small interval of time
• Force per unit area = pressure = equal in all
directions
• Boyle: at constant temperature, the volume of a
fixed mass of gas is inversely proportional to the
pressure applied to it
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 4
∝ GHIJ/) à
pV = constant
Ideal gases
• Pressure Law: pressure of a fixed mass of gas at constant volume is
proportional to temperature as measured on the Kelvin scale:
K
𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 ∝ 𝑇 à - = constant
• Charles’ Law: volume of a fixed mass of gas at constant pressure is
proportional to temperature as measured on the Kelvin scale:
G
𝑣𝑜𝑙𝑢𝑚𝑒 ∝ 𝑇 à - = constant
𝑝4 𝑉4 𝑝O 𝑉O
=
𝑇4
𝑇O
• Double the mass of gas at constant pressure and temperature à volume
doubles
KG
∝ amount of gas enclosed
KG
-
= nR
(where n = number of moles and R is the molar gas constant [J K-1 mol -1])
Univeral Gas Equation
• One mole of any substance includes 6.02 × 1023 atoms/ molecules
• Avogadro number = NA
• Mass of any element containing 6.02 × 1023 atoms = Molar Mass (M)
• One mole of any ideal gas at standard temperature (273 K) and
pressure (1.01 × 105 Pa) occupies 0.0224 m3
• pV = nRT à 𝑅
4.R4×4RT ×R.ROOU V1 /W
= 4×O59
/HI X
= 8.31J𝐾 ^4 𝑚𝑜𝑙 ^4
Molecular Kinetic Theory
• Gas consists of a very large number ’N’ of molecules
• Molecules are moving rapidly and randomly
• Motion described by Newtonian mechanics
• Collisions between the molecules and the walls are perfectly elastic
• No attractive intermolecular forces
• Only intermolecular forces are instantaneous
• Molecules have negligible volume compared to the volume of the
container
1
2
pV= Nm crms
3
• Molecule moving in x direction with a speed ‘u’, elastic collision with wall.
Total change of momentum = (mu) - (-mu) = 2mu
• Time taken to make another collision with the same wall = ‘t’
• Distance travelled = 2l, speed = u à t = _`a
• Rate of change of momentum = change in collision x number of collisions per
unit time
𝑢 𝑚𝑢 O
2𝑚𝑢× =
2𝑙
𝑙
• Rate of change of momentum = force wall exerts on molecule = force
molecule exerts on wall
• There are N molecules moving at different speeds:
/(J< _ dJ_ _ dJW _ d⋯ ) /gJ_
= I
I
• Force =
• Where 𝑢 is the mean square velocity of the molecules moving in the ‘x’
direction
•
•
/gJ_
Force = I
hH*i)
Pressure = j*)1 1
2
pV= Nm crms
3
=
/gJ_
I _×I
=
/gJ_
à
G
pV = mNu2
• We know the molecules are moving uniformly in all directions, with
components of velocity in the x, y and z directions
𝑢O = 𝑣 O = 𝑤 O
(v = speed in y direction, w = speed in z direction)
• cRMS2= root mean square velocity =𝑢 O + 𝑣 O + 𝑤 O = 3𝑢 O
•
•
ilmn _
𝑢 = 9
ilmn_
𝑝𝑉 = 𝑚𝑁 9
O
= nRT
Average Molecular Kinetic Energy
ilmn_
𝑚𝑁 9
•
= nRT (Equation One)
• We know:
• ½ mcrms2 is the KE of one molecule
• EK = ½ Nmcrms2 is the total KE of all the molecules
• Using Equation One: 2EK=Nmcrms2= 𝟑𝟐 nRT
•
•
•
•
Kinetic energy directly proportional to temperature
n = # moles of gas
One mole of gas = NA molecules of gas
Find KE of one molecule…
Wuvw
• Energy ½ mcrms2 = energy of one molecule = _ux
• Average
• Where k
90Ogy
97KE per molecule =
= O
0
= Boltzmann Constant = g
y
y