# On the notion of pressure in the canonical ensemble

1. Jul 17, 2010

### Derivator

Hi folks,

since the volume V is fixed in a canonical ensemble I'm a bit confused about the fact, that the pressure is calculated as the derivation of the internal energy U with respect to the volume V.

Sure, P = dU/dV comes from dU = dQ + dW = tdS - pdV + .... But what does it mean to derivate with respect to the volume, when the volume of the system can't be changed, since it is fixed. (by the way: when the volume is fixed, pdV= p*0 =0, so p is "undefined", since it can take any value.)

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derivator

2. Jul 17, 2010

### Mapes

The volume is not free to change by any significant amount, but we are considering the case where it is changed by an infinitesimal amount. In response, the system energy changes by an infinitesimal amount. The ratio is the pressure.