SR/Piston

Piston Model

KW94 Piston Model

Here we draw principally from the discussion of a simple piston model as presented in §2.7 and §6.6 of [KW94].

An ideal gas of mass $m^{*}$ is held in a vertical container with a movable piston resting on top of — and confining — the gas; the mass of the piston is $M^{*}$. A vertically directed gravitational acceleration, $g$, acts on the piston, in which case the weight of the piston is given by the expression,

$G^{*}=g{M}^{*}.$

"In the case of hydrostatic equilibrium, the gas pressure $P$ adjusts in such a way that the weight per unit area is balanced by the pressure:"

$P=\frac{G^{*}}{A}.$

"If the forces do not compensate each other, the piston is accelerated in the vertical direction according to the equation of motion,"

$M^{*}\frac{d^{2}h}{d{t}^2}=-G^{*}+PA.$

 
 
 
 
 
 
 
 

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