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How is temperature measured?

X. •. X 2. •. X 1. X m. FP 1. FP 2. Temp. Error!. 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.

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How is temperature measured?

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  1. X • X2 • X1 Xm FP1 FP2 Temp. Error! 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.

  2. Ranges of various types of thermometer V P or V n.b.p. = normal boiling point

  3. Reference Points for Older Temperature Scales Daniel Fahrenheit (Danzig (Gdansk)1724) Ice, water and ammonium chloride mixture = 0 °F Human body = 96 °F (now taken as 98.6 °F) Anders Celsius (Sweden, 1742) Boiling point of water = 0 ºC ! Melting point of ice = 100 ºC! Values were later reversed. Scale called “centigrade” Two (or more) reference points result in errors when extrapolating outside of their range.

  4. Pt Resistance Thermometer For 0 ºC < t < 850 ºC Blundell and Blundell, Concepts in Thermal Physics (2006)

  5. - + Unknown temp. (hot junction) V Seebeck effect Principle of Thermocouples Fixed temp. (cold junction)

  6. Metals used for Thermocouples Each type requires calibration against fixed points. Reports on Progress in Physics, vol. 68 (2005) pp. 1043–1094

  7. Spectral Distribution of Thermal Radiation Radiation energy density infrared UV-Vis. Planck distribution law

  8. SB constant Compare radiation flux at an unknown temperature to the flux from a fixed point: triple point of water Thermal Radiation Stefan-Boltzmann equation:

  9. 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.

  10. Fixed Temperature Reference Points Melting points of metals and alloys Reports on Progress in Physics, vol. 68 (2005) pp. 1043–1094

  11. Defining a Temperature Scale with a Single Fixed Point • Requires a linear (monotonic) relationship: X is a thermodynamic variable, Tx is the temperature at which it is measured, and c is a constant. • 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

  12. • 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.

  13. Cell for Establishing the Triple Point of Water Reports on Progress in Physics, vol. 68 (2005) pp. 1043–1094

  14. Defining a Temperature Scale with a Single Fixed Point We see that: So, What thermodynamic variable should be measured to use the thermodynamic temperature scale?

  15. Gas P, V Unknown T TP = 273.16K The Gas Scale of Temperature Ideal gas law: V and n are held constant.

  16. A constant-volume gas thermometer

  17. Relationship between °C and K: °C = K - 273.15 Defining the Kelvin and Celsius scales “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. 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!

  18. Proposed definition of the Kelvin • Temperature scales have been refined as recently as 1990 (International Temperature Scale) • 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!

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

  20. Measuring k with Brownian Motion Sub-mm polymer particles in water Random path his viscosity of fluid phase; ris the particle radius x

  21. 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)

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