Work: Difference between revisions

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The mechanical '''work''', ''W'', performed in ''compressing'' a gas is given by
The mechanical '''work''', ''W'', performed ''upon'' a gas is given by


:<math>W = - \int_\alpha^\beta p ~dV</math>
:<math>W = - \int_\alpha^\beta p ~dV</math>


where <math>\alpha</math> and <math>\beta</math> are points in state space, ''p'' is the [[pressure]]
where <math>\alpha</math> and <math>\beta</math> are points in state space, ''p'' is the [[pressure]]
and ''V'' is the volume.
and ''V'' is the volume. The mechanical work done ''by'' the gas has the opposite sign (a common
source of mistakes).


For reversible changes
For reversible changes, where the system evolves through a succession of equilibrium states, one has


:<math>\left.dW\right.=-p~dV  </math>
:<math>\left.dW\right.=-p~dV  </math>

Latest revision as of 10:22, 5 July 2011

The mechanical work, W, performed upon a gas is given by

where and are points in state space, p is the pressure and V is the volume. The mechanical work done by the gas has the opposite sign (a common source of mistakes).

For reversible changes, where the system evolves through a succession of equilibrium states, one has

and for irreversible changes