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Temperature and Kinetic Theory
Before our current
understanding of heat took
shape, it was believed that
objects heated up because of
a fluid called “caloric”.
Antoine Lavoisier proposed
caloric theory – the idea that
a fluid called “caloric” would
flow from hotter bodies to
colder bodies causing each
of them to experience a
temperature change
French Chemist and
Revolutionary
1743-1794
James Joule disproved caloric theory
(heat as a fluid) by demonstrating a
relationship between heat and work.
It was realized that heat is a form of
energy. But to be that, it couldn’t be a
fluid. Caloric theory was abandoned.
Joule’s Experiment
English Physicist and
Brewer
1818-1889
As a substance warms up, energy is absorbed by molecules
causing them to move faster
Therefore, the average kinetic energy of the molecules
increases.
Most substances expand when they are
warmed because of the excessive
molecular movement.
∆L = αL0∆T
L = Initial length (any unit)
T = Temperature (C)
α = coefficient of linear expansion (C-1)
Three Mechanisms for Energy Transfer
This process of heat transfer through contact is called heat conduction.
Examples:
Cold clothes in your closet get
placed on your warm body
Cold ice cubes are placed
in a warm drink
In each case, the cold object warms up and the warm object cools down
until a temperature in the middle is reached (thermal equilibrium).
Big picture – Energy flows from warm objects to cold objects. This flow
of energy is called heat (Q).
Details – Molecules in the warmer object collide with molecules in the
colder object and transfer their kinetic energy to them
H = Q / t = kA∆T / L
H = rate of heat transfer (W or J/s)
Q = heat (J)
k = thermal conductivity
A = cross-section area (m2)
T = temperature (C)
L = length through which heat is
transferred (m)
Energy can transfer due to
currents caused by pressure
differences.
Warmer molecules carry
energy.
Process called convection
(No contact necessary)
Energy transfer can also be
caused by electromagnetic
waves.
Waves carry energy through
space.
Process called radiation.
(No contact needed, no
substance needed)
Two rooms, each a cube 4.0 m per side, share a 12-cm-thick brick wall.
Because of a number of 100-W light bulbs in one room, the air is at 30 C,
while in the other room it is at 10 C. How many of the 100-W bulbs are
needed to maintain the temperature in the warmer room since heat is
traveling through the wall?
Ideal Gas Laws
An ideal gas is one in which:
•Particles are point particles (only
translational motion)
•All collisions are perfectly elastic
(no KE lost)
•Particles are spaced far apart
•Particles do not attract / repel
each other
•Lots of particles
http://www.cabrillo.edu/~jmccullough/Applets/OSP.html
P1V1 = P2V2
Boyle’s Law (isothermal system)
V1 / T1 = V2 / T2
Charles’ Law (isobaric system)
P1 / T1 = P2 / T2
Gay-Lussac’s Law (isovolumetric
system)
P1V1 / T1 = P2V2 / T2
Combined Gas Law (number of
moles constant)
PV = nRT
P = Pressure (Pa or N / m2)
V = Volume (m3)
n = number of moles
T = Temperature (K)
R = Universal Gas Constant (8.31 J / mol K)
PV = NkBT
N = number of molecules
kb = Boltzmann’s Constant (1.38 x 10-23 J / K)
Temperature is not a measurement of heat.
•Heat is energy that flows from one object to
another. It is not inherent to a specific substance.
•Temperature is.
Temperature – the
measurement of the average
translational kinetic energy of
the molecules that make up a
substance
KEave = 3/2 kBT
KEave = average molecular kinetic energy (J)
kB = Boltzmann’s constant
T = temperature (K)
The average kinetic energy takes
into consideration the speeds of
all the molecules. The speed of
the average molecule is called
the “root mean square speed” or
vrms
Since KE = ½ mv2 for the average molecule
½ mv2 = 3/2 kBT
v2 = 3kBT/m
vrms = √(3kBT/M)
vrms = root mean square speed (v of average molecule)
M = molecular mass (kg)
Calculate the rms speed of helium atoms near the surface of the Sun at a
temperature of about 6000 K.
What is the rms speed of nitrogen molecules contained in an 8.5-m3 volume
at 2.1 atm if the total amount of nitrogen is 1300 mol?
A tank in a room at STP contains 26.0 kg of O2 gas at a gauge pressure
of 8.70 atm. If the oxygen is replaced by helium, how many kilograms
of the latter will be needed to produce a gauge pressure of 7.00 atm?
Laws of Thermodynamics
When energy (heat) flows into an object, the
temperature goes up because:
• The molecules move faster
• The kinetic energy of the molecules
increases
Can you have a temperature increase
without adding heat?
We already know that the kinetic energy of
an object is changed by doing work on the
object.
Work causes objects to move faster (W =
ΔKE)
The same is true for molecules…to make
them move faster without heat, work has to
be done on them.
When work is done on a system
by compressing it…
Work can also be done by a
system when it expands….
The temperature goes up
Causing its temperature to go
down
The internal energy (U = molecular KE and PE) of an object
depends on two things:
• How much heat goes in / comes out of system
• How much work is done on / done by the system
∆U = Q + W
U = internal energy (J)
Q = heat (J)
W = work (J)
This formula represents the First Law of Thermodynamics.
The law states that
A system’s internal energy is equal to the heat added
and the work done on the system.
Observing what heat is doing is relatively easy…
Objects that are warming up
are absorbing heat (+)
Objects that are cooling down
are releasing heat (-)
Observing work being done on or by a system is a little more tricky…
Systems that are
compressed have work done
on them (+)
Systems that expand do
work on their
surroundings (-)
Sign
Conventions
Heat
Work
In
+
+
Out
-
-
Since +W causes the gas to compress, it causes a
decrease in volume
Since –W causes the gas to expand, it causes an
increase in volume.
W = -P∆V
W = work (J)
P = pressure (Pa or N / m2)
V = volume (m3)
An ideal gas is heated and expands at a constant total pressure of 3.0 atm
from 400 mL to 660 mL. Heat then flows out of the gas at constant volume,
and the pressure and temperature are allowed to drop until the temperature
reaches its original value. Calculate (a) the total work done by the gas in the
process, and (b) the total heat flow into the gas.
Types of Thermodynamic Processes
Type of Process
or Step
Definition
Result in
First Law
Examples
Isothermal
∆T = 0, ∆U = 0
Q=-W
Water boiling in teapot
Adiabatic
Q=0
∆U = W
Clouds forming in
atmosphere
Isovolumetric
∆V = 0, W = 0
∆U = Q
Soda pop heating in
car
Isobaric
∆P = 0
∆U = Q + W
= Q - P∆V
Piston moving
because of heated gas
P-V Diagrams
P-V diagrams are used to represent thermodynamic systems.
Temperature lines are hyperbolic because of
PV = nRT
If a system’s number of molecules and temperature remains constant, the
product of the pressure and volume must also be constant.
If piston is
isothermal (∆T =
0), then as heat is
added, work is
done by the
system (Q = - W).
Volume goes up
and pressure goes
down.
Different lines represent
different types of
systems
AD is an isovolumetric
system (V is constant).
AB is an isothermal
system (T is constant)
BD is an isobaric system
(P is constant)
P-V diagrams that are
closed represent cyclical
thermodynamic systems.
Examples
Engines
Refrigerators
We know that
W = -P∆V
On a P-V diagram, work is…
the area under the curve.
Important because it tells
you how efficient
thermodynamic systems
are (i.e. how much energy
is converted to work)
Adiabatic systems
are ones that have
a temperature
change without
heat being
exchanged.
The lines are NOT
hyperbolic like
isotherms.
Consider the following two-step process. Heat is allowed to flow out of an
ideal gas at constant volume so that its pressure drops from 2.2 atm to 1.4
atm. Then the gas expands at constant pressure, from a volume of 6.8 L to
9.3 L, where the temperature reaches its original value. Calculate (a) the total
work done by the gas in the process, (b) the change in internal energy of the
gas in the process, and (c) the total heat flow into or out of the gas.
Heat Engines and Car Motors
Heat engines are designed to use the heat that flows from a high temperature to a
low temperature.
The separation between can either be spatial (different regions) or temporal
(different points in time)
As heat naturally flows from the hot region to the colder region, work is produced.
Steam
Engine
1. Cold water gets heated creating steam (Q in)
2. Steam at high pressure pushes piston creating work (W out)
3. Cold steam condenses creating water (Q out)
4. Water returned to boiler via pump to repeat process (W in)
In an engine, the high temperature
is achieved when a mixture of fuel
and air is ignited by a spark plug.
The gas mixture left over is cooler and
it is pushed out as exhaust.
The expanding gas does work
against the piston pushing it
downward.
The cycle repeats over and over which
turns a crankshaft making the car move
forward
The efficiency of an engine is defined as the
ratio of the amount of work output (W)
relative to the amount of heat input (QH)
e = W / QH
After work is done, there is still heat left over
(QL)
QH = W + QL
Therefore,
e = (QH – QL) / QH
e = 1 – (QL / QH)
Can an engine ever be 100% efficient?
NO! Violation of Second Law of Thermodynamics which states that systems
move toward a greater state of “entropy” or “randomness.” i.e., no device can
transform all of its heat completely into work (Kelvin-Planck statement).
A Carnot engine is
a theoretical design
that gives an
impression of what
an “ideal” engine
would look like.
Because no heat
would be lost as
friction, the
temperature would
be absolutely
proportional to the
heat.
Therefore, the efficiency is calculated using the internal temperatures of
the hot and cold reservoirs rather than the heat flows.
ec = (TH - TL ) / TH = 1 – (TL / TH)
A heat engine utilizes a heat source at 550 C and has an ideal Carnot
efficiency of 28%. To increase the ideal efficiency to 35%, what must be
the temperature of the heat source?
Refrigerators and Air Conditioners
Can heat ever flow from cold regions to warm regions?
YES! But it has to follow the Second Law of Thermodynamics which
states that in order for heat to flow backwards, work has to be done on the
system (Clausius statement)
Refrigerators follow this principle.
Work is done to move heat
(energy) a cold area to a warmer
area. Otherwise, it wouldn’t move
that direction.
What is left is a cold region that
has gotten even colder and a
warm region that has gotten even
warmer.
A compressor does work on
refrigerant vapor making it hotter.
As it moves outside the
refrigerator, it loses heat to the
outside and condenses.
As it moves into the refrigerator,
it expands and becomes a cooler
liquid.
While in the refrigerator, it takes
in heat from the refrigerator and
becomes vaporized.
The compressor does work to
heat it up and move it out
repeating the process.
Both statements of the Second Law of Thermodynamics can be summed up this
way…
Natural systems tend to move toward a greater state of disorder.
Furthermore, although energy is conserved, it becomes less useful
For example,
• A mixture with layers initially cannot be shaken with the expectation that the
layers will be restored.
• A coffee cup that drops and breaks cannot reassemble itself.
• Your room?
When heat flows from hot to cold, the molecules end up all having the same
temperature and kinetic energy (less order). To flow from cold to hot, work has to
be done because that direction would produce more order.
Engines cannot produce the same amount of work as the initial heat because
some of the heat is converted to other less useful forms (internal energy, radiant
energy)