I'm confused, can someone please explain that to me in layman's terms?
I'm not a physicist.
The mathematical aspects of entropy are probably beyond layman's terms. Insofar as the link provided by @Jonas, although it's good, i'm not sure how helpful it would be to a layman.
Probably the most intuitive explanation of the second law and entropy that most folks can understand is rooted in everyday experiences. It has to do with the natural direction of processes. For example we all know
Heat only flows naturally (without help) from hot to cold objects and
Rivers always flow down-hill
And one that you, a biophysics student can relate to:
- People always grow old
These are all examples of what we call irreversible processes (they don't naturally reverse). For each process, entropy is generated. But all of these processes obey the first law of thermodynamics, which is basically conservation of energy.
For example, if heat flowed naturally from a cold object to hot object, the heat lost by the cold object would equal the heat gained by the hot object and energy would be conserved. But we never observe this to happen.
If water flowed naturally up hill it would lose kinetic energy and gain gravitational potential energy and energy would be conserved. But we never observe this to happen.
As far as the third example is concerned, ask your teacher how the second law applies to it.
Scientists (Notably Clausius and Carnot) realized that there must be another law and property governing the direction of processes in addition to the law of conservation of energy. Enter the second law and entropy.
Now as regards to the definition of entropy, the proper form of the equation is
Which says that a differential change in the property called entropy equals a reversible transfer of heat $\delta Q$ divided by the temperature at which the transfer occurs.
Entropy is generated when the heat transfer is irreversible, i.e., when it occurs over a finite temperature difference. This entropy generation may result in the lost opportunity to do work. A mathematical explanation is needed to show how. Your teacher should be able to help.
Hope it helps.