I often see the expression W = V Δ P for the work of a constant volume compression where there are a fixed number of moles and the compression is caused by heating. Is this the work equation for a constant volume, isothermal process where the pressure is increased by adding moles of a gas?

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I often see the expression   W  =  V  Δ  P for the work of a constant volume compression where there are a fixed number of moles and the compression is caused by heating. Is this the work equation for a constant volume, isothermal process where the pressure is increased by adding moles of a gas?

arribanti9 · Accepted Answer

In classical gas dynamics, in order to have work, you need a volume change dV. If volume V is constant, no work is performed.The traditional picture is to think of a piston closing a cylinder containing the gas. The gas inside the cylinder will be characterized by pressure p, temperature T and volume V. To actually perform work, the piston needs to be moved, which implies a change of volume   d  V  =  S    d  x, where S is the moving surface of the piston and dx the distance it moved. Work is then performed by the force pushing the piston, related to pressure by   F  =  p  ⋅  S, and during a slight motion dx of the piston, work performed is   d  W  =  F  ⋅  d  x  =  p    S    d  x  =  p    d  V. Adding work on small motions yields an integral,   W  =  ∫  p    d  VIf volume doesn&#039;t change, no work is performed. Energy may still be transfered into or out of the &quot;cylinder&quot; (whatever the gas&#039; container is), but in a disorderly, non-directional fashion, that is as Heat, not Work.

I often see the expression W=/_\P for the work of a constant volume compression where there are a fixed number of moles and the compression is caused by heating. Is this the work equation for a constant volume, isothermal process where the pressure is increased by adding moles of a gas?

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