9478 / 2027
Temperature and Ideal Gases overview

Lesson 1 of 5

Temperature on an absolute scale

  • I can explain an absolute thermodynamic temperature scale independent of a particular substance's property.Syllabus

    Syllabus 9478, 12(a). Explain an absolute thermodynamic temperature scale independent of a particular substance's property.

  • I can convert between Celsius and thermodynamic temperatures using the 273.15 offset.Syllabus

    Syllabus 9478, 12(b). Convert between Celsius and thermodynamic temperatures using the 273.15 offset.

Make a guess. You are not marked.

A gas is heated from 20 degrees C to 40 degrees C at constant volume. Does its pressure double?

  1. No: the absolute temperature rises from 293 K to just 313 K.
  2. Yes, because pressure is proportional to temperature at constant volume.
  3. It more than doubles, because pressure rises faster than temperature.
Show the answer

No: the absolute temperature rises from 293 K to just 313 K.

Pressure at constant volume is proportional to absolute temperature. 313 / 293 = 1.07, so the pressure rises by about 7%, not 100%.

Temperature determines the direction of net heating when systems are put in thermal contact. Gas equations use an absolute temperature scale, so a Celsius reading must be converted before substitution.

A temperature does not depend on the thermometer's substance

A thermodynamic temperature scale has an absolute zero and is independent of the property of any particular substance. Mercury expansion, electrical resistance and a gas's pressure can all change with temperature. Calibrated thermometers use such properties to indicate the same physical quantity; the choice of material does not define a different thermodynamic temperature.

The SI unit is the kelvin, K, written without a degree symbol. Here T denotes thermodynamic temperature and θ denotes the Celsius reading. Other texts may use T for a Celsius reading too, so read the named quantity and its unit.

Convert a reading, then compare it

T/K = θ/°C + 273.15

This equation relates the numerical readings on the two scales. Absolute zero is 0 K = -273.15°C. A reading of 26.85°C corresponds to 300.00 K.

The same temperature has two different readings

Matching levels represent the same physical temperature. Both scales use the same linear spacing: a change of 1 K has the same size as a change of 1 °C.

Celsius and kelvin scales have equal intervals and an offset of 273.15Two aligned vertical scales use 0.9 drawing units per kelvin or degree Celsius. From the bottom, matching pairs are zero kelvin and minus 273.15 degrees Celsius; 273.15 kelvin and zero degrees Celsius; 300 kelvin and 26.85 degrees Celsius; and 360 kelvin and 86.85 degrees Celsius. The absolute-zero level is the bottom of the thermodynamic scale. The 300-to-360-kelvin interval is the same height as the 26.85-to-86.85-degree-Celsius interval. Equal interval sizes do not make temperature ratios interchangeable between the two scales.Celsiusθ / °CKelvinT / K-273.1500273.1526.8530086.85360Absolute zero: 0 K

From 300 to 360 K, the rise is 60 K. The Celsius rise is also 60 °C, but gas-law ratios must use the absolute readings in kelvin.

Aligned marks represent the same physical temperatures on two scales. Equal-sized intervals do not make the absolute readings or their ratios interchangeable.

A temperature interval of 1 K is the same size as an interval of 1°C. The 273.15 offset cancels when two readings are subtracted, but it does not cancel when their ratio is taken.

Worked temperature comparison

Warming from 20.00°C to 40.00°C

T1 = 293.15 K; T2 = 313.15 K
ΔT = 313.15 - 293.15 = 20.00 K
T2/T1 = 313.15/293.15 ≈ 1.068

The temperature rise is also 20.00°C, but the absolute temperature has increased by about 6.82%, not doubled. Use the kelvin ratio in ideal-gas and mean-particle-energy comparisons.

Check your understanding

A gas warms from 20.00 degrees C to 40.00 degrees C. Which statement correctly describes its temperature change and absolute-temperature ratio?

  1. The change is 293.15 K and the absolute-temperature ratio is 40.00/20.00, which is 2.
  2. The change is 20.00 K and the absolute temperature doubles.
  3. The change is 20.00 K; the ratio is 313.15/293.15, about 1.068.
Show the answer

The change is 20.00 K; the ratio is 313.15/293.15, about 1.068.

Celsius and kelvin intervals have equal size. The 273.15 offset cancels in a difference but must be included in each absolute temperature before taking a ratio.

Interpret a thermometer reading

For a contact thermometer, establish good thermal contact and wait for a stable reading before using it as the object's temperature. Select a suitable range, record the scale or display resolution and check calibration. The surroundings' temperature is not automatically the temperature of an object that is still warming or cooling.

In the classical ideal-gas model, mean translational kinetic energy tends to zero as T tends to zero. This does not establish that every possible microscopic motion in every real material stops. Likewise, extending an ideal-gas graph to 0 K does not show that a real gas stays gaseous and ideal all the way there.