# 7.003 Zeroth Law, Temperature Scale, Ideal gas Eqn

“It is the only practical theory of universal content, which I an convinced, that within the framework of applicability of its basic concepts will never be overthrown”

– Albert Einstein

Now since we are though the rules, Let’s start the Game.

We will take every statement of every law, analyse it how do we get to it or how did people at those days observed it, where it is applied, what are future scope etc.

STATEMENT – If two bodies A and B are at Thermal equilibrium and another pair B and C are in Thermal Equilibrium then there exist thermal equilibrium between A and C.

What does the thermal equilibrium means?

The simple language, when two bodies have the same temperature they are said to be at thermal equilibrium. Now since the thermodynamics is actually just having laws based on observation we must follow a few things that we can easily observe-

Heat flow from higher to lower temperature, but before that

How do we know which body is hot and which is cold?

This is something interesting for the class, let’s go back in the early 1800’s and try to think what it was like.

To define the scale for any measurement we are going to require

• Some property related to the quantity we want to measure
• Some standard reference point, dependent on no or least possible factors.

The temperature scales in early 1800 were like, the Fahrenheit scale of temperature

–Property uses was expansion of liquid taken (like Hg) which was depending on the property (temperature) we want to measure.

–The standard reference point was freezing point of water and the temperature of body of a healthy man, yes these were the first two reference point and the interpolation was linear.

I.e. the volume of Hg increase is linearly dependent on the temperature change.

The numbers we allot to measure the temperature numerically, were 320F for freezing point of water and 960F for body temp in mouth of a fit man.

Obviously, Both the references were, not the best choice human body temperature and boiling point depends on lot of things like impurities, surrounding, temperature, pressure etc.

Celsius Scale

Now Celsius scale has same procedure but references were different and he used something known to us as the Boyle’s Law

Lim (PV/n)t = K (constant) = f(t)   function of  temperature (at p->0)

Best part for these references were that they were not depending on the Gas, independent of the gases taken. Substance taken was water again and the references were freezing and boiling point of water at 1bar pressure.

Now we were having to property, f(t),references  boiling point of water and freezing point of water i.e. two numerical values i.e. Value 00C and 1000C. Drawing the graph considering linear interpolation.

Looking at the extended line of the graph we have an amazing result there, Since the f(t) cannot have negative value as none of pressure or volume being negative make any sense.

So we conclude that No matter what we cannot go below -273.150C.

That was something basic of Kelvin scale at least the numerical values, for Kelvin scale he had

T(K) = T0C + 273.15 that is something that we use for conversion,

Now that substance was water and the triple point was the reference

273.15K at pressure 6.1X10-3 bar (triple point is where all three phase coexist)

And other was the 0K called as absolute zero.

The temperature is also referred as absolute temperature in Kelvin only, the value in any mathematical formula that we use is in Kelvin only. Graph is just as a bit shifted

Mathematically,

The simplest eqn    Y=m*X (line passing through origin)

Considering the above case we can write the eqn as following,

Since the slope value is constant for every gas we replace it with some constant (say R)

So we have     f(T) = R.T

Lim (PV/n)t = RT (at p ->0 the condition say that real gases behave ideally at low temperature)

Here from we have the very famous ideal gas equation,

Are gases ideal?

I can bet if they were we would have been in a lot of trouble practically and the thermodynamics would have been completed with this question so,

NO, not a single one of them is ideal.

But then why to study all about ideal gases, because almost every gas have a temp range in which it behave ideally, and other reasons are taught in detail in course 4.000

Abhishek kumar jha

(Chemistry at Utkarshini)