Carnot Engine - Thermodynamics ( Physics Remix)

Carnot Engine?

"Wait, Why not bikenot engine? Why not busnot? Why not Planenot ? Why only carnot?"

< Listen , if you are thinking of these kind of questions too , first I would advice you to close your book, get some sleep and then stress about your finals again after a good rest 😂>

------------------------------ Few hours later ------------------------------

Slept well? Yup, me too . Your head not pounding about finals anymore is it? Okay, now lets start 🤯

Let's start with the very basics

What is an heat engine?

An engine is a machine which converts power into motion ( kinetic motion). An Heat Engine, is basically a device by which a system is made to undergo a cyclic process that results in conversion of heat to work.

Cars, planes, washing machines, everything around you which do mechanical work have engines in them. We also know that not all of it is transformed hundred percent as useful work. The fuel in car engines don't hundred percent get converted to make the car work, some get wasted into other forms

Carnot, a scientist, devised an ideal engine which is based on the fundamentals of thermodynamics ( and that's where we got the name "carnot engine" 😬)

It is based on a reversible cycle of four operations in succession

a) Isothermal expansion

b) Adiabatic expansion

c) Isothermal compression

d) Adiabatic compression

But before we go in deep about these four processes, lets discuss the main parts of Carnot's engine

Source of heat

It's a hot body or reservoir of very large capacity kept at a constant high temperature T1. ( Its upper surface is perfectly conducting so that working substance can take heat from it)

The System and Working Substance

It's usually a hollow cylinder whose walls are perfectly non-conducting and has a piston. This piston moves without any friction. Ideal gas enclosed in cylined is the working substance.

Heat Sink

It is a cold body at low temperature T2.

and an Insulating stand

The Mechanism

a) Isothermal Expansion

First the cylinder is taken to be in thermal equilibrium with the source of heat. This initial state of working substance is denoted by (P1, V1, T1). This happens isothermally, as the piston is allowed to moved very slowly . Heat from the reservoir passes into the cylinder while the temperature remains T1. Finally the gas expands and receive heat Q1 from source and gets to state (P2,V2,T1)

The Heat input Q1 is utilised to for doing work W1 ( no change in internal energy)

b) Adiabatic Expansion

Now Cylinder is placed on the non-conducting stand, and piston is allowed to move outwardly adiabatically ( no release or absorption of heat). The temperature falls to T2 and reaches (P3,V3, T2)

During this expansion, more work done (W2) is at the expense of internal energy

c) Isothermal Compression

The Cylinder is placed in contact with the sink at T2. The piston is moved slpwly inward so that the heat produced is passed to the sink. The gas isothermally reached (P4,V4,T2)

W3 , Work done will be equal to the amount of heat given to the sink

d) Adiabatic compression

The Cylinder is again placed on the insulated ( non-conducting) stand. The piston moves inside, heat doesn't go out hence internal energy of the system is increased. It again reaches the state (P1,V1,T1)

This cycle of operations is called the legendary "Carnot Cycle"

Things to notice :- In the first two steps, work is done by engine, hence W1 and W2 are positive

In the next two steps, work done is done on gas , hence W3 and W4 are negative

< Now wait, you might be thinking, "How the heck is random exchange of heat between two complicated thingamabobs making the car move?"

All this exchange is leading to one important thing - Motion of the PISTON! , yes that stick on top of our gas cylinder which kept dancing up and down. That motion can be used to turn wheel or a set of gear which will lead to the satisfaction of the work needed to be done>

THE CARNOT THEOREM

We did the entire procedure above under idealised conditions, we used frictionlenss pistons, ideal gases and reversible processes , which is basically not possible in the practical world. Hence, there can be no engine having better effeciency than Carnot Engine, no engine better than the carnot engine ( thought it might sound like Carnot was a stuck up big head , what he said was true )

Refrigerator

The Refrigerator, the almighty machine because of which ice cream exists, works on the similar principles. It follows the similar procedures but in reverse.

It extracts heat from the colder reservoir due to external work and deposits it into the hot reservoir.

The efficiency formula is the exact opposite as that of a heat engine

Now instead of ending this blog with the usual memes, am ending it with a very weird question

> If you leave the door of a refrigerator open in a well insulated room, what will happen to the temperature in the room?

Answer - THE TEMPERATURE INCREASES!

Nope, it doesn't cool down. The heat dissipated from the back of the frigde will be more as it takes the entire room as its cool reservoir, hence more energy is dissipated than absorbed.