Introduction To Heat, Internal Energy And Work

Introduction to Heat

We are quite familiar with the term heat that can be described as feeling too hot or too cold.

We know that the sun is the main source of the earth’s heat.

Only a fraction of the sun’s heat reaches the earth which is sufficient for life to exist on earth.

What happens if the intensity of sun rays reaching the earth increases?

We would start feeling hot and prefer to stay at home and sit under the AC.

Now, the question arises why we feel hot outside and cold under the AC?

So, the chill we feel is because of the flow of heat.

What is Internal Energy?

We know that temperature is the measure of the molecular kinetic energy of the particles in a system.

This kinetic energy is distributed amongst the translational motion, rotational motion, and vibrational motion of a molecule.

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There is also molecular potential energy by the electromagnetic force acting upon the atoms of an individual molecule and between each separate molecule.

The sum of all these energies exhibited by the particles of a system is called the internal energy of the system denoted by the letter U.

This energy is associated with atomic motion and is directly proportional to the temperature of the system.

So, higher is the temperature, higher is the internal energy, and vice versa.

What is Internal Energy of a System?

The internal energy of a system can be increased by increasing the heat transfer, but because of factors such as surface deformation, friction, there may be some energy loss.

We learned that for a particular system, there will always be a conservation of energy.

Let’s say, a stone is falling freely under gravity, it possesses both potential energy and kinetic energy.

So, let’s add internal energy of the objects to this list, and restate conservation of energy with the equation below:

                                     ΔPE +ΔKE +ΔU = 0

Here,   ΔPE = change in potential energy

            ΔKE = change in kinetic energy, and

            ΔU = change in internal energy

So, if any of these quantities change, then some energy is transformed from one form to another.

Internal Energy Formula

Consider an ideal gas:

Its total energy = Internal energy because of the kinetic energy of molecules.

Its potential energy is zero because there is no attraction between the molecules.

So, TE = 0 + KE

Using the First Law of Thermodynamics

Consider a thermodynamic system having an ideal gas packed under the piston:

On adding Q amount of heat to this system, several factors of gas increments:

1. Molecular speed 

2. Heat and temperature

3. Pressure

The piston moves upward; it means some work is done by this thermodynamic system to bring the piston up.

Here, this thermodynamic system absorbs heat. It retains a part of heat with itself and uses another part by working in raising the piston.

The part of heat absorbed by the system increases its internal energy.

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The internal energy was U1 after piston rise; the internal energy is U2 and U2 > U1.

So, the change in internal energy is:

ΔU = U2 - U1

Here, ΔU is the heat retained by the system, and 

W  = The work done by the system to raise the piston.

So, Q (Amount of heat provided) = ΔU + W

Why the system kept ΔU instead of U2?

Because the heat absorbed by this system got converted to the work done in raising the piston and only a difference of the energy got by the system.

This is how we got the formula, Q = ΔU + W.  

In differential form:

                     მQ = მU + მW…..(1)

Relation Between Enthalpy and Internal Energy

We define enthalpy as the heat content of a system at constant pressure.

We know that: H = U + PV

This relationship says:

Heat content in the system is equivalent to the internal energy of molecules or atoms (PE + KE) at quantum level + PV (the work done to establish the system at external pressure P and volume V from space.

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So, work done can be seen in this diagram.

The unit of enthalpy is KJ/mol. 

In thermodynamics, H has no significance; let’s understand why?

If we go at the microscopic level to estimate the amount of energy each molecule possesses, it becomes an impossible task to do so.

Like we can’t measure the quality of a person like singing but can compare by the number of awards you won (Quantifying). Similarly, we can’t measure the energy absorbed by the system.

Therefore, to consider H as an enthalpy, it becomes a matter of confusion.

So, that’s why we study ΔH in place of H.

So, ΔH and ΔU instead of H and U.

Since the volume expanded from V1 to V2

At constant pressure equation becomes:

 ΔH = U + P (V2 - V1) 

 ΔH = U + PΔV

At constant volume: ΔH = U + VΔP…(2)