Thermal Equilibrium and Temperature

Learn about : Thermal Equilibrium and Temperature (Zeroth law of Thermodynamics) , Macroscope & Microscopic Descriptions ♦

In analyzing physical situation we usually focus our attention on some portion of matter which we separate, in our minds, from the environment external to it. We call such a portion the system. Everything outside the system which has a direct influence on its behaviour we call the environment

Example – A ball can be the system and the environment can be the air & the earth. In free fall, we seek to find how the air and earth affect the motion of the ball.

In all such cases we much choose suitable observable quantities to describe the behaviour of the system. We classify these quantities as Macroscopic (like pressure, volume, temperature for example) and Microscopic (Here, we consider quantities that describe the atoms and molecules that makeup the system, their speeds, energies, masses, angular momenta, behaviour during collisions, etc.)  Thus macroscopic quantities form the basis of science of thermodynamics. While the microscopic quantities form the basis of science of statistical mechanics.

Thus for any system, the microscopic and macroscopic quantities must be related because they are simply different wrap of describing the same situation.

Example : Let us take open tube mercury monometer connected to a gas tank, the pressure of a gas viewed macroscopically, is measured using a manometer. If it is viewed microscopically it is related to the average rate per unit area at which the molecules of the gas deliver momentum to the manometer fluid as they strike its surface

   Thermal Equilibrium (The Zeroth law of Thermodynamics)

Let us consider an object A which feels cold to the hand and identical object B which feels hot and let both be placed in contact with each other. After a sufficient length of time, A and give rise to the same temperature sensation. Thus A and B are said to be in thermal equilibrium with each other.

We can generalize the expression : Two bodies are in thermal equilibrium, to mean that the two bodies are in states such that if the two are connected, the combined system would be in thermal Equilibrium. The logical test for thermal equilibrium is to use a third body such as a thermometer. This is summanized in a law called “the zeroth law of the thermodynamics”

STATEMENT : If A and B, two objects are in thermal equilibrium with a third body C (The ‘Thermometer’)s then A and B are in thermal equilibrium with each other.

Thus, a scalar quantity, temperature, which is a property of all thermodynamic systems (in equilibrium states), such that any two systems having the same temperature must be in thermal equilibrium with each other
Example :- If shows two system A and B separated by an adiabatic wall (a wall which does not allow heat flow)

The two systems are placed together with third system C with a diathermic wall (a wall which permits heat flow) in between. Suppose A, B, C are at different temperatures. Systems A & C, B & C will be exchanging heat with each other, after certain length of time, they will attain thermal equilibrium with each other separately. It the adiabatic wall is removed between A and B at that time, it will be found there will be no exchange of heat between  the systems A and B. Therefore, the system A and B are allowed to attain thermal equilibrium separately with the system C.

 Temperature : The degree of  hotness of a body is called its temperature.

As we know that bodily sensation of warmth and cold is not reliable. Suppose we place our right     hand in hot water and the left hand in cold water. If after a few minutes, we place our both the hands in water at room temperature it will be found that to the right hand, the water will appear cold, while   to the left hand the same water will appear hot. Hence our judgment of temperature can be rather     misleading. Further, the range of our temperature sense is limited. What we need is an objective, numerical, measure of temperature.

An instrument used to measure the tempearture of a body is called a thermometer .
 HEAT When two systems at different temperatures are placed together, the final temperature reached is in between the two starting temperature. This has a common observation upto the beginning of the nineteenth century, it was considered that a material substance ‘Caloric’ existed in every body. It was believed that a body at high temperature contained more caloric than one at a lower temperature. This caloric is nothing but heat, which is transferred between a system and its surroundings as a  result of temperature difference only.

 ♠ Heat is a form of energy which produces in us the sensation of warmth.

Example : a piece of burning charcoal is known to be very hot, while Ice cube is very cold.

When bodies are heated, physical changes are likely to develop like change of state, (from solid to liquid incase of ice cube) expansion, (on heating gas expands as molecules have more kinetic energy), contraction etc.

Heat is a form of energy. For example, when we heat the gas in a container by burner it expands as the kinetic energy of the molecules increases due to heat imported to it which causes expansion. Hence, Heat energy is converted into kinetic energy which is nothing but mechanical energy. Thus, energy can be changed from one form to another form.

In 1978, Count Rumford engaged in making a bore in the brass cannon observed that the drilling tool became hot. Also, the brass chips cut off from the barrel of the cannon produced a sufficient increase in the temperature of the water on following in it (to prevent over heating, the bore of the cannon was kept full of water). The water was replenished as it boiled away during the boring process. In order to explain the production of heat during the drilling process, according to early caloric theory, when a metal cut into fine chips, the heat squeeze out from the body. It implied that the heat of the metal is the form of chips less than its value, when it is in the form of block. However, experiments conducted by Rumford proved that there is no difference in the values of specific heat of metal in two cases. It led to the downfall of caloric theory