Many modern technologies, such as computers and smartphones, are built on the principles of Physics Topics such as quantum mechanics and information theory.
What are Fixed Points in Temperature?
An instrument that measures the temperature of a body is called a thermometer.
From zeroth law we see that, to determine the thermal equi-librium between A and B [Fig.], a third body C can be used as a reference body. In this case C acts as a thermome-ter.
Temperature scale: A scale of temperature is needed to measure the temperature of a body accurately. To draw up a scale we follow the norm that a hot body is at a higher tem-perature while a cold body is at a lower temperature. It implies that when a hot and a cold body are in contact, tem-perature of the hot body will decrease and that of the cold body will increase. When the temperatures of both the bodies become equal, the bodies attain thermal equilibrium.
Fixed point: To set up a temperature scale, one or more conveniently reproducible, well-established temperatures are chosen as standard temperatures. These fixed temperatures are called the fixed points.
Primary thermometer: There are several kinds of ther-mometers for practical use. There are liquid thermometers (mercury or alcohol), ideal gas thermometer, platinum-resis-tance thermometer etc. Among these, there is a special kind of thermometer which is used to deduce the accurate value of different fixed points. This is known as primary thermom-eter. Using these fixed points, other thermometers are cali-brated.
The universally accepted primary thermometer is the ideal gas thermometer. The thermometer contains a gas, under ideal conditions, kept at a constant volume. The prop-erty of the gas, that changes with temperature, is its pressure. As such, pressure is called the thermometric property of the gas. The thermometer is also known as a constant volume gas thermometer. To fix the ideal gas temperature scale, the temperature (T) is assumed to be proportional to the pressure (p) of the gas. So,
T ∝ p, or, T = kp, where k is an unknown constant.
To know the value of k, one fixed point should be chosen and its temperature allotted with a definite value. This fixed point, known as the fundamental fixed point, is the triple point of water (discussed below). The value of its tempera-ture is universally accepted as 273.16. Later, Kelvin intro-duced a thermodynamic temperature scale, which exactly coincides with the ideal gas scale. So the unit of temperature is chosen as kelvin or K; then the temperature of the triple point of water is T0 = 273.16 K.
Triple point of water: The triple point of water is the state at which ice, water and water vapour can coexist in thermal equilibirum. At this state, the pressure and the temperature are fixed; so it is a fixed point. The value of pressure at this fixed point is 4.58 mm of Hg; the value of temperature is assigned as 273.16 K in the ideal gas scale (see the chapter ‘Change of State of Matter’).
Unless a very accurate value of temperature is required, we may use the number 273 in place of 273.16 for the triple point of water. In that case, C = K – 273; so that practically there is no difference between the values of triple point of water and ice point (see the table below).
Ideal gas scale: Scaling of the ideal gas thermometer is done considering the triple point of water as 273.16. Then temperatures of a few more fixed points are measured using this scale. The scale obtained from this is called ideal gas scale. Nowadays, Kelvin (K) is used as the unit instead of degree kelvin in ideal gas scale.
The following table fists some of the important fixed points and their temperatures; mesured and ascertained by an ideal gas thermometer. All fixed points other than the triple point of water are called the secondary fixed points.
Secondary thermometer: All thermometers, other than the ideal gas thermometer, are secondary thermometers. They are called secondary because they are calibrated according to the values of temperatures of fixed-points already determined by an ideal gas thermometer. So all secondary thermometers actually obey the ideal gas temperature scale. However, it should be noted that, the secondary thermometers should never be regarded as less reliable or less efficient. Rather, they are often highly accurate and very easy to use. The most important of them are liquid thermometer and resistance thermometer.
The four scales of temperature—Celcius, Fahrenheit, Reaumur and Kelvin : Fixed points and symbols:
Equivalence of the temperatures recorded in the four different scales mentioned above: Let C, F, R and K be the temperature of a body as recorded in three different scales viz., Celsius, Fahrenheit, Reaumur and Kelvin respectively. Then,
\(\frac{C-0}{100-0}\) = \(\frac{F-32}{212-32}\) = \(\frac{R-0}{80-0}\) = \(\frac{K-273}{373-273}\)
or, \(\frac{C}{5}\) = \(\frac{F-32}{9}\) = \(\frac{R}{4}\) = \(\frac{K-273}{5}\)
Equivalence of the temperature recorded in any two different scales : Let the temperature of a body in scale A be p and that in scale B be q. Then,