Monday, March 20, 2017

Reversibility of a thermodynamic process

If one wants to understand thermodynamic entropy, he/she should start from reversibility.

What is reversibility of a thermodynamic process? Let us start from a thermodynamic process and then move on to define reversibility.

A system is said to have undergone a thermodynamic process if it changes its state from initial state to final state. State of a system is referred by its coordinates under thermodynamic equilibrium condition. Typically, state of the system is identified by the state variables, aka, thermodynamic properties such as pressure, temperature, density, etc.

A process is said to be a reversible process if the system reverses its direction by changing from final (new initial) state to initial (new final) state. The beauty of a reversible process is it brings system  back to its original state tracing the same path.

Now what is the big deal about reversibility? It is very hard to achieve. In some cases, it is even impossible.

Are you wondering why should we learn reversibility then? Well, there is certainly a reason to it. In thermodynamics, our aim is to build engines that takes energy in available form (heat) and convert it to useful form (work). Thermodynamics first law gives us the assurance that this is indeed possible. However, first law falls short in providing the limit to this conversion which depends on quality of energy. But how can one quantify quality of energy?

It is quite a challenge to quantify quality of energy. Quality is a relative term. What I consider to be of high quality may not be the same for someone else. With this ambiguity, how can we address this issue scientifically? Understanding reversibility can through us some light on our discussion. Reversible process is difficult to achieve, but such a process can act as a reference against which actual processes can be compared with.

The following example may make the concept more clear. Suppose let us say I have a pen (system) and paper (surroundings) and I intend to write a letter (work). At the end of the writing process, I would have spent a certain amount of ink fluid in order to get the writing done. Now the pen has changed its state from its initial (full ink) state to final (partial ink) state. To bring back the system to its initial state again, I have two choices.
  • Extract the ink embedded on the paper and supply the same quantity to pen. This will bring back the pen and paper (system and its surroundings) to their original state making this process a totally reversible one.
  • Take an ink pot. Fill the pen with quantitatively same amount of ink which was spent as work. In this case, only the system comes back to its initial state, while surroundings went through a permanent change. Such a process is called as internally reversible process.

Quantitatively, there is no difference between the two choices. However, quality of ink from ink pot and that from a paper are different. Ink from ink pot can be used to do more work, while ink of same quantity from paper can never be recovered. The change in quality of energy is due to reversibility of the process. At best, one can strive to achieve a process that comes closer to a reversible process.

This brings us to the closure of this lecture.

Take home message: One way to quantify quality of energy is by comparing an actual process to its reversible equivalent.