First law of thermodynamics equation (A practical explanation)

Equation of first law of thermodynamics is mentioned below. 

First law of thermodynamics equation

Let me tell you my own story.

When I was a student like you, I was really stuck with this confusing equation. 

I was not getting the exact idea what this equation wants to say. 

Then I studied from various sources (books, internet, as well as from my teacher), and finally I got the exact idea with a practical example.

Now I will explain the same, in easy way. 

In fact the example which I have mentioned here makes me remember this first law of thermodynamics equation and statement very easily. 

So let’s get started with the example.

Before that, here is a statement of first law of thermodynamics in terms of heat, work and internal energy.

“First law of thermodynamics: The net change in the total energy of a system (∆E) is equal to the heat added to the system (Q) minus work done by the system (W).”

Don’t worry, let’s take an example to understand this complicated statement.

first law of thermodynamics equation using example of muscular boy taking energy drink

You can see in this picture that the muscular boy is taking energy drink which is having Q amount of energy. 

Thus we can say that Q amount of energy is entering the body.

first law of thermodynamics in which muscular man is showing biceps animated

After taking the Q amount of energy, this muscular boy is now ready to do work. He is feeling energetic and he has now total energy of E1.

animated exhausted body builder doing weight lifting

Now this picture shows that this muscular boy has lost some of his energy in doing the work (here weight lifting). After doing this work, his energy decreases to E2. 


Now, let me explain these things with some equations. 

It’s easy. Don’t worry. 

Now here,

Q = Inlet energy to the body

W = Outlet energy in the form of work

E1 = Total energy that boy is having during initial state

E2 = Total energy that boy is having during the final state

Here, the body gains Q amount of energy as shown in the above image. And after sometime the body is spending some W amount of energy in doing work.

Hence the net change in total energy of the body is given by Q – W.

I told you guys that the boys total energy was E1 and then it became E2. Thus, this change in total energy is nothing but E2 – E1.

Above statement can be mathematically written as;

E2 – E1 = Q – W

Therefore, ∆E = Q – W

This equation is known as the equation for first law of thermodynamics.

equation of first law of thermodynamics
in terms of internal energy

Now, you will easily understand the statement of the first law based on this equation. 

“First law of thermodynamics: The net change in the total energy of a system (∆E) is equal to the heat added to the system (Q) minus work done by the system (W).”

In the above equation, the total energy ∆E is nothing but a sum of kinetic energy, potential energy and other energies present in the molecules of the body, which is also known as internal energy ∆U.

I’ve explained all these things later in this article. Don’t worry.

I have also explained the sign convention for work (W) and heat (Q). You will come to know when we should take the sign of work and heat as positive (+ve) and negative (-ve).

Keep reading.

What is heat (Q) in the equation of first law of thermodynamics?

heat conduction example in which a boy is touching a hot stove gets injured animated

What happens when you touch a hot dish in a kitchen?

You feel it hot. But what exactly happens here?

It’s a flow of heat energy from the hot dish to your hand. 

It’s a flow of heat energy from the higher temperature body to a lower temperature body.

That’s it !!

Now let us define heat.

Definition of heat:

Heat is defined as a flow of thermal energy due to differences in temperatures.

Heat is simply thermal energy in transit.

Very easy, isn’t it?

Sign convention of heat(Q) in the equation of first law of thermodynamics

When should we take the sign of heat (Q) as positive and when we should take it as negative?

negative sign of heat when it is rejected from the system in sign convention of heat and work in thermodynamics

When the heat is lost from the system, then we have to take Q as -ve. (Remember, if heat is going then minus sign) 

positive sign of heat when it is rejected from the system in sign convention of heat and work in thermodynamics

When the heat is supplied to the system, then we have to take Q as +ve. (Remember, if heat is coming then plus sign).

What is work (W) in the equation of first law of thermodynamics?

During the thermodynamic process, the volume of the system may increase or decrease.

Due to this increase or decrease in the volume, the thermodynamic work appears here.

But how will you decide whether the system is doing work on the surrounding or surrounding is doing work on the system?

Who is doing work on whom?

Don’t worry, I’ll make you understand this.

Let’s consider a piston cylinder assembly as shown below.

work done by the system of piston cylinder arrangement showing expansion of piston due to heat supply

You can see that when heat is supplied to the system, then its volume increases. 

Let;

V1 = initial volume of the system

V2 = final volume of the system

P = constant pressure of the system

See, here the pressure of the system remains constant because, as heat is supplied, the volume increases and thus the pressure remains constant or maintained inside the system.

The work done by the system can be obtained from following formula;

                   W = P (V2 – V1)

                        = P ∆V

Sign convention of work (W) in the equation of first law of thermodynamics

work done is positive when volume of the system increases

When the volume of the system increases, then we have to take sign of work W as +ve. This is a work done by the system. (Remember: Volume increases then plus sign for work)

work done is negative when volume of the system increases

When the volume of the system decreases, then we have to take sign of work W as -ve. This is a work done on the system. (Remember: Volume decreases then minus sign for work)

What is Internal energy in first law of thermodynamics equation?

internal energy of molecules in the equation of first law of thermodynamics

There are small atoms in all the substances which possess various types of motion.

These motion can be;

  • Rotational motion
  • Vibrational motion
  • Translational motion
types of motion in molecules indicating rotational motion, vibrational motion, and translational motion

As these molecules are in motion inside the substance, the energy possessed by them is called kinetic energy.

attractive and repulsive forces in molecules indicate the molecular potential energy

The molecules also possess attractive and repulsive forces. These forces indicate the potential energy between them.

Now, internal energy is nothing but a sum of all these molecular kinetic energy and molecules potential energy.

what is internal energy in first law of thermodynamics equation

I hope you have understood everything about the first law of thermodynamics equation. Let me know in the comments if you have any queries.

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