How is temperature measured?• T measurement is not based on a fundamental physical unit.

• Use a thermodynamic parameter (X) that varies in a known way with temperature.

• Measure its value at TWO fixed points of temperature and then interpolate and extrapolate.

X

Temp.

•

•

FP2FP1

X1

X2

Error!

Xm

n.b.p. = normal boiling point

Ranges of various types of thermometer

V

P or V

Reference Points for Older Temperature Scales

Daniel Fahrenheit (Danzig (Gdansk)1724)

Anders Celsius (Sweden, 1742)

Boiling point of water = 0 ºC !

Melting point of ice = 100 ºC!

Values were later reversed. Scale called “centigrade”

Ice, water and ammonium chloride mixture = 0 °F

Human body = 96 °F (now taken as 98.6 °F)

Two (or more) reference points result in errors when extrapolating outside of their range.

)++1(= 20 BtAtRRt

For 0 ºC < t < 850 ºC

Pt Resistance Thermometer

Blundell and Blundell, Concepts in Thermal Physics (2006)

Fixed temp.

(cold junction)

+ -Unknown temp.

(hot junction)

VSeebeck effect

Principle of Thermocouples

Reports on Progress in Physics, vol. 68 (2005) pp. 1043–1094

Metals used for Thermocouples

Each type requires calibration against fixed points.

Radiation energy density

Planck distribution law

T1∝max

infraredUV-Vis.

Spectral Distribution of Thermal Radiation

4423

45

=15

2= TT

ch

kR

Stefan-Boltzmann equation:

Thermal Radiation

( )4=TPWTT

TPWRR

Compare radiation flux at an unknown temperature to the flux from a fixed point: triple point of water

SB constant

Black Body Radiation from Au at its Melting Point

Used to calibrate pyrometers.

See presentation by Mark Owen at the Professional Training conference to hear about pyrometry at NPL.

Reports on Progress in Physics, vol. 68 (2005) pp. 1043–1094

Fixed Temperature Reference Points

Melting points of metals and alloys

xcTX =

Defining a Temperature Scale with a Single Fixed Point

X is a thermodynamic variable, Tx is the temperature at which it is measured, and c is a constant.

• Requires a linear (monotonic) relationship:

• Also requires a single fixed point. There are several possibilities!

• By international agreement* in 1954, the so-called “thermodynamic temperature scale” uses the triple point (TP) of water defined - not measured! - to be 273.16 K.

*Tenth General Conference on Weights and Measures

•0.006

The Triple Point of Water

At the triple point of water: gas, solid and liquid all co-exist at a pressure of 0.006 atm.

Reports on Progress in Physics, vol. 68 (2005) pp. 1043–1094

Cell for Establishing the Triple Point of Water

Defining a Temperature Scale with a Single Fixed Point

K

T

cT

cT

XX x

TP

x

TP 16.273==

)(16.273=TP

x XX

T

We see that:

What thermodynamic variable should be measured to use the thermodynamic temperature scale?

So,

( ) cTTP VnR ==

TPTP PP

KTK

TPP

16.273=⇒16.273

=

The Gas Scale of Temperature

Ideal gas law:

TP = 273.16KUnknown T

GasP, V

V and n are held constant.

A constant-volume gas thermometer

°C = K - 273.15Relationship between °C and K:

Defining the Kelvin and Celsius scales

Note that careful measurements find that at 1 atm. water boils at 99.97 K above the melting point of ice (i.e. at 373.12 K). 1 K is not exactly equal to 1 °centigrade!

“One Kelvin degree is 1/273.16 of the temperature of the triple point of water.”

Named after William Thomson (Lord Kelvin) who was a professor at the University of Glasgow.

Proposed definition of the Kelvin

• Recognising that thermal energy is given by kT (where the Boltzmann constant is k = 1.38065 x 10-23 JK-1), the Kelvin could be defined simply as:

“The kelvin is the change of thermodynamic temperature that results in a change of thermal energy kT by 1.38065XX × 10−23 Joule.”

This definition requires a very precise measurement of k!

• Temperature scales have been refined as recently as 1990 (International Temperature Scale)

Reports on Progress in Physics, vol. 68 (2005) pp. 1043–1094

R = NAk

Measuring k with Brownian Motion

x rkT

tx

D6

=6

><=

2 is viscosity of fluid phase;

r is the particle radius

Random path

Sub-m polymer particles in water

Third Law of Thermodynamics

Planck: The entropy of all systems is the same at 0K and may be taken to be zero.

A temperature of 0 K is unattainable in a finite number of steps.

Blundell and Blundell, Concepts in Thermal Physics (2006)