# Why is the change in entropy greater for processes occurring at lower temperatures? [duplicate]

We have the thermodynamic definition of entropy $\Delta S = q_{rev}/T$. If heat transfer is the same for both processes at different temperatures, this implies that the same process occurring at lower temperature would generate more entropy than if the process occurred at higher temperature. Why is this the case? Why isn't the change in entropy equal for both processes?

## marked as duplicate by Gert, ACuriousMind♦, user36790, Kyle Kanos, user10851 Nov 9 '15 at 7:37

• – Gert Nov 1 '15 at 2:49
• I'm looking for an intuitive explanation rather than a mathematical one... – notorious Nov 1 '15 at 4:15
• In many cases, this formula (or the equivalent in terms of Carnot processes) is taken as the definition of (absolute) temperature. If you want an explanation of this formula, you have to tell us how you want to define temperature in the first place... – Fabian Nov 1 '15 at 21:13
• You might be able to avoid this getting closed as a duplicate if you make it explicit that you want an intuitive picture rather than equations. Still, as noted by @Gert, this really was asked already and has a reasonably good answer. – DanielSank Nov 3 '15 at 9:32
• The second link (Why does heat added to a system...) explicitly asks for intuition. – user10851 Nov 9 '15 at 7:39

If you are looking for an intuitive explanation for this, as you said in the comments above, I'll try to give you one here.

We assume an heat transfert is done in a high temperature environment, which means the entropy of this environment is already high since particles are already more agitated and that the energy is dispersed in a disorded way. Now if we imagine the same heat transfert in a low temperature environment, where the entropy is initially lower, we could say that the impact on the entropy of this heat transfert is more important than the same heat transfert in the high temperature environment since the energy that has been transfered in the low temperature environment makes up a greater part of the overall energy.

Sorry if I am unclear, it seems logical to me, but it is quite hard to explain. Let me give you a simpleexample with numbers.

If we have the high temperature environment with an initial energy of 100 and the low temperature environment with an initial energy of 10 (no matter the units, the one you want). If the energy transfert is of 5 in the same units then we can calculate that this heat transfert increases the energy in the high energy environment by 5% and increases the energy by 50% in the low energy environment. So we see that the same heat transfert influences more the low temperature environment than the high temperature one.

Hope you see what I mean, ask me questions if some things are unclear.