# Entropy Qrev/T?

by aniketp
Tags: entropy, qrev or t
 Sci Advisor HW Helper PF Gold P: 2,532 Hi aniketp, One way of writing the First Law is $$dU=q+w$$ which means that the differential change in energy equals the heat transferred to a system plus the work done on a system. But another way is $$dU=T\,dS-p\,dV$$ where the work is expressed as a generalized force (pressure) times a generalized displacement (change in volume). The heat transfer term is expressed in an analogous way: a generalized force (temperature) times a generalized displacement (change in entropy). If you haven't heard the terms generalized force and generalized displacement before, they're just ways to classify variables. Generalized forces are intensive, and they drive processes; a change in temperature drives heat flow, and a change in pressure drives mass flow. Generalized displacements, which are extensive, are the "stuff" that is transferred: entropy, volume. $S=Q_\mathrm{rev}/T$ arises because at constant volume and temperature, and if the process is reversible (no excess entropy generated) we can integrate $q=T\,dS$ to give $Q_\mathrm{rev}=T\Delta S$. Does this make sense?