1.0 Introduction

1.1 Thermometers

It is the 'Energy in transition due to the temperature difference. When transfer of heat takes place, the temperature of one body increases and the temperature of the other body decreases, except in a particular case where the phase transition takes place.

If a system $A$ is in thermal equilibrium with system $B$ and the system $B$ is in thermal equilibrium with system $C$, then the systems $A$ and $C$ are in thermal equilibrium with each other.

The common property of these systems in thermal equilibrium is the temperature. Thus, the temperature of a system is the property of which determines whether or not the system is in thermal equilibrium with other systems.

It is a device that is used to measure the temperature. All the thermometers works on the principle that some physical properties of a system changes due to the change in temperature. some physical properties that changes with temperature are

The thermometer we use in everyday life consists of a mass of a liquid, usually mercury or alcohol that expands in glass capillary tube when heated. In this case the change in volume of the liquid is the physical property.

Thermometric property is a property that can be used to measure the property. It represents a physical quantity that varies linearly with temperature like length, volume, ...etc. Let $X$ denotes the physical quantity, ${X_0},{X_{100}},{X_t}$ be its values at ${0^o}C$, ${100^o}C$ and ${t^o}C$. Then, $$t = \left( {\frac{{{X_t} - {X_0}}}{{{X_{100}} - {X_0}}}} \right) \times {100^O}C$$(1) Constant volume gas thermometer : The pressure of a gas at constant volume is the thermometric property, $$t = \left( {\frac{{{P_t} - {P_0}}}{{{P_{100}} - {P_0}}}} \right) \times {100^O}C$$(2) Mercury thermometer : The length of a mercury column from some fixed point is taken as fixed point.$$t = \left( {\frac{{{l_t} - {l_0}}}{{{l_{100}} - {l_0}}}} \right) \times {100^O}C$$(3) Platinum resistance thermometer : The resistance of the platinum wire is the physical property.$$t = \left( {\frac{{{R_t} - {R_0}}}{{{R_{100}} - {R_0}}}} \right) \times {100^O}C$$

Question 1. A platinum resistance thermometer reads ${0^O}C$ when its resistance is $80\Omega $ and ${100^O}C$ when its resistance is $90\Omega $. Find the temperature at which the resistance is $86\Omega $.

The temperature on the platinum scale is $$t = \frac{{{R_t} - {R_0}}}{{{R_{100}} - {R_0}}} \times {100^O} = \frac{{86 - 80}}{{90 - 80}} \times {100^O} = {60^O}$$