11 Apr 2025

From the dynamic theories of Heat as a fluid to its utmost idea of heat as the kinetic energy of molecules, thermodynamics has come a long way defining how we'd look at different ways to interpret Motion, Heat, Conductivity and Temperature. From a dog following Newton's law of cooling by squeezing its body in the winter to a human being studying heat and its relations with friction, to land a space capsule: it is of our best interests to use thermodynamics in our day-to-day life.

In the terms of thermodynamics, two terms Specific Heat Capacity and Cubical Expansion are common. It is interesting to learn and use these terms for different calculations. These terms can be used to calculate the very fundamentals of heat and its nature. 

Recently though, I have stumbled across a very general question onto how can two different terms in Thermodynamics: Specific Heat and Cubical Expansion be related in any way other?

When asked to my professor, he replied with an answer not so satisfactory and when asked to the internet, it gave no information what-so-ever. 

Therefore, when I took the matter into my hands and started playing around the formulae I discovered a way to relate these two terms in a surprising manner. And something that was even more surmising was that it showed relations with four postulates of my combined equation that defined a lot of theoretical ideas in the field of thermodynamics. 

Here is the detailed idea of my analysis and theoretical experiments leading to the AN.T's Equation or Tripathi's Equation. 

 1) Theoretical  IDEA 

               Fig – (i)                                                          Fig – (ii)

Let a cube of any material where its Initial Mass = m : Initial Volume = V₁   : Specific Heat Capacity = S  and Cubical Expansion = g ; be heated from Initial Temperature = t₁   to  Final Temperature = t₂ .

And

V₂ be the final volume of the solid after heating and Q is the total heat transferred between burner and solid. 

Let, 'dt' be the change in temperature from t₁  to   t₂ .

Now,

• For General Cubical Expansion : 

                   
or,

or,   ------------------------------------ (1)

• For Heat Consumption by solid :

 or,  

or,                  ---------------------------------- (2)

 Now, 

• For the formation of AN.T's Equation;

 Combining (1) and (2), we get

 ------------------------- (3)

 This is the general equation for the relation of Specific heat capacity and Cubical Expansion of the solid object. However, with some observation and logical arguments we can obtain the following results. 

From (3) : 

  where,

 Now, with the idea of "Heat per mass" and "Ratio of volume increased by original volume", we don’t need to worry about mass of the body and the expanded volume. 

For every set of there will be only one set of for that same material and same original values of mass (m) and volume (V₁).

2) Postulates or Results 

1. Relation between Heat Transferred and Volume Increased:

  From,    ,

 From the above relation, we can see that and  are constants. This means,

 I.e. the amount of heat transferred per unit mass is directly proportional to the increased volume per original volume.

In other words, more the heat supplied more the expansion. 

2. The ratio of g to s is the ratio of "Heat transferred per mass" by "Rate of volume increased ".

Which means, “The ratio of set of every unit mass that gets heated and its volume expansion is the ratio of its specific heat capacity and its cubical expansion."

2. Ratio of "Specific Heat Capacity " and "Cubical Expansion" is always smaller than the ratio of "Total heat " and   "Final Volume" , when heated.

 Logically,

Therefore, the equation becomes:                                                

So, the ratio of total heat and final volume is always greater than the ratio of specific heat capacity and cubical expansion, when the object is heated i.e. V₂ >V₁.

3. THE OPEN QUESTION: 

For and being the ratios, can we exclaim that for one particular set of entries i.e. for one value of Q, m, V₁  and V₂ ;
 

Conclusion: 

Therefore, in this way: I turned a physics inquiry that had been itching me for a month or so, to one of the most beautifully crafted relations of physics. 

Curiosity meets Knowledge to experience Intelligence. 

With the ending notes of this article, I want to attract few eye balls of policy makers from the ministry of education to induce learning patterns that really touches the inner nerves of Students and suggests him to think out of the box.