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Physics LibreTexts

1.2: Thermometers and Temperature Scales

  • Page ID
    4345
  • Figure shows Farhenheit, Celsius and Kelvin scales. In that order, the scales have these values: absolute zero is minus 459, minus 273.15 and 0, freezing point of water is 32, 0 and 273.15, normal body temperature is 98.6, 37 and 310.15, boiling point of water is 212, 100 and 373.15. Zero degree F is minus 17.8 degree C and 255.25 degree K. The relative sizes of the scales are shown on the right. A difference of 9 degrees F is equivalent to 5 degrees C and 5 degrees K.

    Figure \(\PageIndex{2}\): Relationships between the Fahrenheit, Celsius, and Kelvin temperature scales are shown. The relative sizes of the scales are also shown.

    Figure \(\PageIndex{2}\). Temperatures on these scales can be converted using the equations in Table \(\PageIndex{1}\).

    Table \(\PageIndex{1}\)
    To convert from…Use this equation…
    Celsius to Fahrenheit\(T_F = \frac{9}{5}T_C + 32\)
    Fahrenheit to Celsius\(T_C = \frac{5}{9}(T_F - 32)\)
    Celsius to Kelvin\(T_K = T_C + 273.15\)
    Kelvin to Celsius\(T_C = T_K - 273.15\)
    Fahrenheit to Kelvin\(T_K = \frac{5}{9}(T_F - 32) + 273.15\)
    Kelvin to Fahrenheit\(T_F = \frac{9}{5}(T_K - 273.15) + 32\)

    To convert between Fahrenheit and Kelvin, convert to Celsius as an intermediate step.

    Example \(\PageIndex{1}\): Converting between Temperature Scales - Room Temperature

    “Room temperature” is generally defined in physics to be \(25^oC\). (a) What is room temperature in \(^oF\)? (b) What is it in K?

    Strategy To answer these questions, all we need to do is choose the correct conversion equations and substitute the known values.

    Solution

    To convert from \(^oC\) to \(^oF\), use the equation

    \[T_F = \dfrac{9}{5}T_C + 32. \nonumber\]

    Substitute the known value into the equation and solve:

    \[T_F = \dfrac{9}{5}(25^oC) + 32 = 77^oF. \nonumber\]

    Similarly, we find that \(T_K = T_C + 273.15 = 298 \, K\).

    The Kelvin scale is part of the SI system of units, so its actual definition is more complicated than the one given above. First, it is not defined in terms of the freezing and boiling points of water, but in terms of the triple point. The triple point is the unique combination of temperature and pressure at which ice, liquid water, and water vapor can coexist stably. As will be discussed in the section on phase changes, the coexistence is achieved by lowering the pressure and consequently the boiling point to reach the freezing point. The triple-point temperature is defined as 273.16 K. This definition has the advantage that although the freezing temperature and boiling temperature of water depend on pressure, there is only one triple-point temperature.

    Second, even with two points on the scale defined, different thermometers give somewhat different results for other temperatures. Therefore, a standard thermometer is required. Metrologists (experts in the science of measurement) have chosen the constant-volume gas thermometer for this purpose. A vessel of constant volume filled with gas is subjected to temperature changes, and the measured temperature is proportional to the change in pressure. Using “TP” to represent the triple point,

    \[T = \dfrac{p}{p_{TP}}T_{TP}.\]

    The results depend somewhat on the choice of gas, but the less dense the gas in the bulb, the better the results for different gases agree. If the results are extrapolated to zero density, the results agree quite well, with zero pressure corresponding to a temperature of absolute zero.

    Constant-volume gas thermometers are big and come to equilibrium slowly, so they are used mostly as standards to calibrate other thermometers.

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    Contributors

    • Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).