In reversible process, why define δ W = − P d V instead of δ W = − V d P ?

Question

In reversible process, why define   δ  W  =  −  P  d  V instead of   δ  W  =  −  V  d  P ?

sekanta2b · Accepted Answer

Every system is defined by a variety of extensive variables: entropy, volume, mass, charge, surface area, magnetization, etc. The internal energy U is a function of these variables

U = U (S, V, N, Q, A, M, \dots)

and we seek to know how U changes when the variables change:

d U = {(\frac{\partial U}{\partial S})}_{V, N, Q, A, M \dots} d S + {(\frac{\partial U}{\partial V})}_{S, N, Q, A, M \dots} d V + {(\frac{\partial U}{\partial N})}_{S, V, Q, A, M \dots} d N + \dots .

We happen to call one of these coefficients,

{(\frac{\partial U}{\partial V})}_{S, N, Q, A, M \dots}

, the negative pressure

- P

. We can increase the energy of a system for positive values of

- P d V

. That’s why the parameters are ordered the way they are.

In reversible process, why define δW=−PdV instead of δW=−VdP?

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