Constant Volume Gas Thermometer

Thermometers are working examples of the zeroth law of thermodynamics. The significance of constant volume gas thermometers is that they are used to calibrate other thermometers.

A constant volume gas thermometer is composed of a bulb filled with a fixed amount of a dilute gas that is attached to a mercury manometer. A manometer is a device used to measure pressure.

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From the Law of Gay-Lussac, we know that when the temperature of an ideal gas increases, that there is a corresponding increase in pressure. Conversely, when the temperature decreases, so does the pressure. Constant volume gas thermometers operate on the same principle, with the restrictions that the gas is at low pressure and the temperature of it is well above that of liquefaction.

For a pressure P, the equation used to find the temperature T is

1) T = aP + b

where a and b are constants determined from two fixed points, such as ice at 0^oC and steam at 100^oC.

As mentioned previously, the constant volume gas thermometer uses values from the triple point of water to calibrate other thermometers. To recall, 273.16 K (Kelvin) is the temperature where water exists in an equilibrium state as a gas, liquid, and solid. For equation 1, where a = 273.16 K, b = 0, P_tp is the pressure of the gas at the triple point of water, and P is the pressure of the gas at the temperature to be measured, we have

2) T = 273.16 K (P/P_tp)

For low pressure and high temperatures, where real gases behave like ideal gases, equation 1 becomes:

3) T = 273.16 K lim P/P_tp as P_tp → 0

The gas bulb is inserted into a bath or place we wish to find the temperature of, such as water. When the temperature increases or decreases, the volume also increases or decreases as well as the pressure, as we have seen in Charles' Law and the aforementioned Gay-Lussac's Law. The pressure of the mercury also changes such that it begins to move up or down and thus away from the reference point.

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Figure 2 shows an example from Henry Sostmann's Fundamentals of Thermometry text. A helium filled bulb is placed into a water and steam bath that is at 100^oC. The mercury at the reference point is 1 Pa (Pascal), while that of the reservoir is at approximately 1.367 Pa. The difference between these two is used to help calculate the temperature of the bath.

Physics for Scientists and Engineers by Douglas Giancoli

Physics For Scientists and Engineers by Raymond Serway

Image Credits

Constant Volume Gas Thermometer by Dr. Doug Davis Department of Physics Eastern Illinois University

Figure 2 from Henry Sostmann's Fundamentals of Thermometry Part One (659K PDF File)

• Constant Volume Gas Thermometer Demo
• Constant Volume Gas Thermometers and Calibration
• International Temperature Scales