# JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Thermometers

Thermometers

Category : JEE Main & Advanced An instrument used to measure the temperature of a body is called a thermometer.

It works by absorbing some heat from the body, so the temperature recorded by it is lesser than the actual value unless the body is at constant temperature. Some common types of thermometers are as follows

(1) Liquid (mercury) thermometers : In liquid thermometers mercury is preferred over other liquids as its expansion is large and uniform and it has high thermal conductivity and low specific heat.

(i) Range of temperature : $\underset{\text{(freezing point)}}{\mathop{-\,50{}^\circ C}}\,\text{ to }\underset{\text{(boiling point)}}{\mathop{350{}^\circ C}}\,$

(ii) Upper limit of range of mercury thermometer can be raised upto ${{550}^{o}}C$ by filling nitrogen in space over mercury under pressure (which elevates boiling point of mercury).

(iii) Mercury thermometer with cylindrical bulbs are more sensitive than those with spherical bulbs.

(iv) If alcohol is used instead of mercury then range of temperature measurement becomes $-{{80}^{o}}C$ to ${{350}^{o}}C$

(v) Formula : $t=\frac{l-{{l}_{0}}}{{{l}_{100}}-{{l}_{0}}}\times 100{}^\circ C$

(2) Gas thermometers : These are more sensitive and accurate than liquid thermometers as expansion of gases is more than that of liquids. The thermometers using a gas as thermoelectric substance are called ideal gas thermometers. These are of two types

(i) Constant pressure gas thermometers

(a) Principle $V\propto T$ (if P = constant)

(b) Formula : $t=\frac{V-{{V}_{0}}}{{{V}_{100}}-{{V}_{0}}}\times 100{}^\circ C$ or $T=273.16\frac{V}{{{V}_{Tr}}}K$

(ii) Constant volume gas thermometers

(a) Principle $P\propto T$          (if V = constant)

(b) Formula : $t=\frac{P-{{P}_{0}}}{{{P}_{100}}-{{P}_{0}}}\times 100{}^\circ C$ or $T=273.16\frac{P}{{{P}_{Tr}}}K$

(c) Range of temperature :

Hydrogen gas thermometer :  $-{{200}^{o}}C$ to ${{500}^{o}}C$

Nitrogen gas thermometer :   $-{{200}^{o}}C$ to ${{1600}^{o}}C$

Helium gas thermometer :     $-{{268}^{o}}C$ C to ${{500}^{o}}C$

(3) Resistance thermometers : Usually platinum is used in resistance thermometers due to high melting point and large value of temperature coefficient of resistance.

Resistance of metals varies with temperature according to relation. $R={{R}_{0}}(1+\alpha t)$ where $\alpha$ is the temperature coefficient of resistance and t is change in temperature.

(i) Formula : $t=\frac{R-{{R}_{0}}}{{{R}_{100}}-{{R}_{0}}}\times 100{}^\circ C$ or $T=273.16\frac{R}{{{R}_{Tr}}}K$

(ii) Temperature range :  For Platinum resistance thermometer it is $-{{200}^{o}}C$ to ${{1200}^{o}}C$

For Germanium resistance thermometer it is 4 to 77 K.

(4) Thermoelectric thermometers : These are based on ?Seebeck effect? according to which when two distinct metals are joined to form a closed circuit called thermocouple and the difference in temperature is maintained between their junctions, an emf is developed. The emf is called thermo-emf and if one junction is at ${{0}^{o}}C,$ thermoelectric emf varies with temperature of hot junction (t) according to $e=at+b{{t}^{2}};$ where a and b are constants. Thermoelectric thermometers have low thermal capacity and high thermal conductivity, so can be used to measure quickly changing temperature   Different temperature range

 Thermo couple Temperature range Copper-iron thermocouple ${{0}^{o}}C$ to ${{260}^{o}}C$ Iron-constantan thermocouple ${{0}^{o}}C$ to ${{800}^{o}}C$ Tungsten-molybdenum thermocouple ${{2000}^{o}}C$ to ${{3000}^{o}}C$

(5) Pyrometers : These are the devices used to measure the temperature by measuring the intensity of radiations received from the body. They are based on the fact that the amount of radiations emitted from a body per unit area per second is directly proportional to the fourth power of temperature (Stefan's law). (i) These can be used to measure temperatures ranging from ${{800}^{o}}C$ to ${{6000}^{o}}C$.

(ii) They cannot measure temperature below 800°C because the amount of radiations is too small to be measured.

(6) Vapour pressure thermometer : These are used to measure very low temperatures. They are based on the fact that saturated vapour pressure P of a liquid depends on the temperature according to the relation $\log P=a+bT+\frac{c}{T}$

The range of these thermometers varies from 0.71 K to 120 K for different liquid vapours. .

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