The gauge measures the air pressure inside the hollow metal sphere. Heating the sphere with the Méker burner increases the pressure.
The apparatus shown above comprises a hollow metal sphere connected to a gauge that reads the absolute gas pressure inside the system. That is, if we were to evacuate the apparatus, the gauge would read zero. The gauge reads in units of pounds per square inch, usually abbreviated “psi,” or in this case, “psia,” for “pounds per square inch, absolute.” (Pressure measured relative to atmospheric pressure is referred to as “gauge pressure,” and the units are psig, for “pounds per square inch, gauge.”) The nipple directly opposite the rod that holds the apparatus to the handle, contains a relief valve. In case ambient temperature changes enough to cause the pressure inside the unit to deviate noticeably from atmospheric pressure, pressing this relief valve equalizes the pressure inside the apparatus with the outside pressure. As shown in the photograph, at room temperature the reading corresponds to a pressure of one atmosphere, which at sea level, on average, equals 14.7 psi. In other units, this equals 101,325 pascals (N/m2) or 760 torr (mm of mercury).
In accord with Boyle’s law, for a given mass of gas held a constant temperature, the pressure it exerts on the wall of its container is inversely proportional to the volume it occupies (PV = c; c is a constant), and in accord with the law of Charles and Gay-Lussac, for a given mass of gas held at constant pressure, the volume it occupies is directly proportional to the temperature (V = cT; c is a constant). If we combine these two laws, we find that for a given mass of gas, if we hold the volume constant, the pressure the gas exerts on the walls of the vessel is proportional to the temperature, or P = cT; c is a constant. This means that we can use a fixed volume of gas as a thermometer, hence the name of this demonstration. The typical constant-volume gas thermometer comprises a glass vessel connected to a manometer, constructed in such a way that either one side of the manometer or an auxilliary tube connected to it can be raised or lowered to keep the volume of the gas constant. The apparatus in this demonstration uses a pressure gauge whose working element is a Bourdon tube. This is a flattened tube, bent into a circular shape, perhaps about 3/4 of a circle, closed at one end. The open end is fixed to the piece that connects it to the line in which the pressure is to be measured, and the closed end is attached to a mechanism that operates the needle of the gauge. As the pressure inside the tube increases, the tube straightens slightly, causing the needle to rotate. When pressure is released, the tube returns to its original shape, rotating the needle to its original position. The change in volume this introduces is virtually nil. This apparatus is thus a constant-volume gas thermometer.
From the relations given above, it follows that the pressures at two different temperatures are related by T1/T2 = P1/P2. If we choose some reference temperature Tref , then T/Tref = P/Pref , and T = Tref (P/Pref). For the Kelvin scale, this reference is the triple point temperature of water, which is 273.16 K. (The pressure of the water vapor at the triple point is 4.58 torr.) Our equation thus becomes T = 273.16 K (P/Ptr), where Ptr is the pressure of the gas at the triple point temperature of water. This assumes that the gas behaves ideally; that is, that the interactions among the gas atoms or molecules do not cause the relationship between the pressure and the temperature to deviate from this equation. The lower the gas pressure, the closer its behavior becomes to that of an ideal gas. The ideal gas temperature scale is thus defined as T = 273.16 K limPtr→0 (P/Ptr). We cannot, of course, use such a thermometer at temperatures near that at which the gas becomes a liquid. Still, gas thermometers may be used over a fairly wide range, over which the ideal gas temperature scale agrees with the Kelvin scale. The zero on the Kelvin scale is absolute zero; no temperatures can exist below this.
Other temperature scales are in also in common use. The unit for the Celsius scale is the degree Celsius (°C), which is the same size as the kelvin. This scale is related to the Kelvin scale by the equation TC = T - 273.15°, where T is the temperature in kelvins and TC is temperature in °C. In the Celsius scale, the triple point temperature of water is 0.01 °C, the ice point (at atmospheric pressure) is 0.00 °C, and the steam point (at atmospheric pressure) is 100.00 °C. The Fahrenheit scale is related to the Celsius scale by the equation TF = 32 + (9/5) TC. In the Fahrenheit scale, the degree is 5/9 the size of the Celsius degree, the ice point of water is 32 °F, and the steam point is 212 °F. Perhaps less commonly used than these is the Rankine scale. In this scale the degree is the same size as the degree Fahrenheit, but zero is absolute zero. The Rankine scale is related to the Kelvin scale by the equation TR = (9/5) T, and to the Fahrenheit scale by TR = TF + 459.67 °F. In this scale the ice point of water is 491.67 °R, and the steam point is 671.67 °R.
An interesting note regarding the Kelvin scale
As noted on the page for demonstration 04.06 -- 1-kg mass, 1-meter stick, timer, in 1967, the 13th General Conference of Weights and Measures decided that the SI unit for the thermodynamic temperature scale would be the kelvin, and that its value would be the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. (See CGPM: Comptes rendus de la 12e réunion (1968), page 19.) As of 2019, the kelvin is now defined by taking the Boltzmann constant k to be 1.380649 × 10-23 when it is expressed in units of J/K, which equal (kg·m2)/(s2·K), where the kilogram, meter and second are defined in terms of h, c and the frequency of the transition between the two hyperfine levels of the ground state of the cesium-133 atom. (See Current definitions of the SI units, The redefinition of the SI units and SI-Brochure-9.pdf, p. 133.)
References:
1) Sears, Francis Weston and Zemansky, Mark W. College Physics, Third Edition (Reading, Massachusetts: Addison-Wesley Publishing Company, Inc., 1960), Chapter 15.
2) Resnick, Robert and Halliday, David. Physics, Part One, Third Edition (New York: John Wiley and Sons, Inc., 1977) pp. 459-466.