Thermodynamics.
Study of temperature, heat and related macroscopic properties
of objects and matter.
Specifically macroscopic properties: temperature, pressure,
heat, internal energy…
Thermodynamic equilibrium: two systems are in thermodynamic
equilibrium with each other, when they are in thermal contact
and no change in any macroscopic property occurs with time.
What do we mean by thermal contact?
“Any macroscopic property” – length, volume, pressure,
electrical conductivity, color.
Why do we stress that we talk about MACROSCOPIC properties?
Two systems have the same temperature if they are in
thermodynamic equilibrium.
Temperature is the parameter that two systems in
thermodynamic equilibrium have in common.
Zeroth law of thermodynamics:
if two systems A and C each are in thermodynamic equilibrium
with system B, then A and C are in thermodynamic equilibrium
with each other.
Sounds trivial, but gives a rationale for measuring temperature.
Zeroth law of thermodynamics:
if two systems A and C each are in thermodynamic equilibrium
with system B, then A and C are in thermodynamic equilibrium
with each other.
B
A
C
Liquid thermometers
Based on thermal
expansion of liquids.
The liquids are held in
little vessels at the
bottom.
At higher temperatures
they expand and climb
toward the top of
narrow capillaries.
How to calibrate a liquid thermometer?
You need some reference
temperatures.
You may want to stick the
thermometer into boiling water
and melting ice, hoping that
those set two well-defined
temperatures.
You will find the liquid expanded
and its column risen.
What next?
We can divide the column height difference into N (say, N = 100) even
intervals and call them degrees.
Would it be a good temperature scale?
Would it be the same, no matter what liquid we use?
Liquid thermometers
Coefficients of thermal expansion
!V / V
"=
!T
β – fractional increase of
volume per one degree
Problems:
1. Liquid is a rather complex state of matter. Molecules in liquids are
held together by cohesive forces, different for different liquids.
2. The coefficients of thermal expansion vary a lot between liquids,
and may depend on temperature in an extreme fashion.
3. Liquids freeze at low temperatures and boil at high temperature. So
the ranges of operation of the liquid thermometers are restricted.
Gas thermometer
Basically, a gas thermometer is like a barometer measuring
absolute pressure of a gas in a closed volume.
Gas thermometer
Gasses are much simpler than
liquids.
The molecules are moving freely
most of the time, and only once in
a while suffer short term collisions.
The collision events are still
different for different molecules….
BUT: when the gasses are rarified (low density) and the collisions are rare
the behavior of different gasses in the gas thermometer becomes very
much the same!
In order not to change the gas density, it is preferable to keep the gas
volume constant and to measure the gas pressure.
Gas thermometer
Level of the mercury in
the right tube is varied to
keep the level in the left
tube constant.
Pressure of the gas is
measured as P =ρgh
The absolute temperature of the
system is defined as:
P
T = 273.16
P3
P3 is pressure of the gas at a special reference point called “triple
point”, which is unique and can be reproduced in every laboratory.
Gas thermometer
To set the temperature scale we
need some convenient reference
points.
273.15 K, the same as 0 °C is
the temperature of ice melting at
normal pressure;
373.15 K, the same as 100 °C is
the temperature of water boiling at
normal pressure;
1K temperature difference is the same as 1 °C temperature
difference, but 0 K corresponds to -273.15 °C.
Temperature scales
Fahrenheit
Celsius
Lord Kelvin
9
TF = 32° + TC
5
TK = 273.15 + TC
Thermometers: summary.
1. Thermometers always measure their own
temeparature.
2. For a thermometer to measure the
temperature of the system of interest, it
needs to be brought into thermal
equilibrium with the system (and better
insulated from everything else).
•
•
A thermometer must be much smaller than system.
For fast temperature measurements, it should be small, have good
thermal conductivity and low heat capacity.
An array of miniature
thermometers
An array of bolometers
Heat is not a material or a from of matter.
Heat is energy in transit!
When pouring water
you transfer it from
one vessel to
another and you get
more water in the
second vessel.
In thermodynamics you transfer heat but you usually end up
having more or less internal energy.
Heat is positive when the system of interest obtains it.
What are common results of heat transfer?
1. Growth of temperature.
2. A phase transition (melting ice).
3. Mechanical work.
In cases #2 and #3 there may be NO temperature variation.
Case #1, no phase transition or work done.
How much does the temperature vary?
Heat capacity of the object C, measured in J/K;
tells you how much Joules of heat you need to transfer to
increase the temperature of the object by 1 K (or 1 ºC).
!Q
C=
!T
!Q = C!T
Heat is energy in transit! Positive, when obtained.