Entropy Reversibility

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I don't get this concept at all.
I am also confused on what entropy is at all. I have always thought of it as the measure of disorder but this seems to be only one of the definitions.
Maybe it's because I'm not sure what entropy is that I am having a problem with understanding reversibility.
I was thinking that it meant that if it was possible, the system must change by the environment and the change much be very small and it would take an infinite amount of time. Though...I'm not sure why it has to be tha way.
However, delta S is defined as reversible Q/T in an isothermal process
This is where I get confused on the meaning of the statement. How can the reversibility
[My mind is really scattered right now so I'm sorry if this isn't super coherent]
 

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A cup of tea gets cooled in an environment from a temperature of 50°C to 25°C. What is the process involved..

The cup of tea (System) is at a temperature of 50 °C and the room air (Surrounding) is at a temperature of say 25°C. Now Heat flows from high temperature to low temperature. So heat is rejected from Tea (system) to the room air (Surrounding) due to a finite temperature difference of 30 °C. And a finite time it attains a Temperature of 25 °C. This process you just saw is called as Irreversible - Definition - A process which occurs due to finite difference of Temperature/Pressure/Concentration. All the process in this world are irreversible.

Now I am going to explain you how this tea can be cooled reversibly from 50 °C to 25 °C in a reversible manner.

For this you need to have a Room Air (surrounding) whose temperature can be controlled by you.

Now initially you have to Set the room temperature as 49.99, So that there is a infinitesimal temperature difference of 0.01 degree centigrade between tea (System) and room Air (Surrounding). Hence an infinitesimal amount of heat will be rejected from Tea to room Air, making the temperature of the tea to decrease to 49.99 °C. Now heat transfer will stop as both system and the surrounding will be at same temperature i.e. 49.99 °C. Now you need to decrease the Room Air Temperature again by an infinitesimal amount to 49.98 °C. Again infinitesimal amount of heat will be rejected from Tea which is at 49.99 °C to room air which is at 49.98 °C. And finally both the System and Surrounding will be at the same temperature of 49.98 °C (System and Surrounding are again in Equilibrium) .Like wise you have to repeat this steps unit both system and surrounding reaches a temperature of 25°C. What we have done is almost called as reversible Process (Actually a quasi static Process)

Now I want you to understand the differences between the two processes (Reversible and Irreversible) .

1. When Tea was cooled Irreversibly- The process took finite time.
When it was cooled reversibly it took infinite time.

2. When Tea was cooled irreversibly the system and surrounding need not be in equilibrium during the process (i.e. at any point of time during the process we cannot say that temperature of tea is equal to the temperature of air.

However in a reversible process after every step the temperature of tea was equalized to temperature of the surrounding, thue after every step there was an equilibrium between system and surrounding.

3. Thus we can say in a perfect reversible process, all the states passed by system are equilibrium states. But it is not so in a irreversible process.

4. As you saw reversible process is very difficult /impractical and impossible to carry out. However all the process occurring in the world are irreversible process which are easy to happen.

I hope you got some understanding about reversible and irreversible process with the above explanation.

But it does not end here.

I advise you to watch Video Lectures by SK SOM - Thermodynamics in NPTEL to learn more.
 
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