SR/Piston: Difference between revisions
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Here we draw principally from the discussion of a simple piston model as presented in §2.7 and §6.6 of [<b>[[Appendix/References#KW94|<font color="red">KW94</font>]]</b>]. | Here we draw principally from the discussion of a simple piston model as presented in §2.7 and §6.6 of [<b>[[Appendix/References#KW94|<font color="red">KW94</font>]]</b>]. | ||
An ''[[SR# | An ''[[SR#Equation_of_State|ideal gas]]'' of mass <math>m^*</math> is held in a vertical container with a movable piston resting on top of — and confining — the gas; the mass of the piston is <math>M^*</math>. A vertically directed gravitational acceleration, <math>g</math>, acts on the piston, in which case the weight of the piston is given by the expression, | ||
<div align="center"><math>G^* = g M^*.</math></div> | <div align="center"><math>G^* = g M^*.</math></div> | ||
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<div align="center"><math>P = \frac{G^*}{A}.</math></div> | <div align="center"><math>P = \frac{G^*}{A}.</math></div> | ||
<font color="darkgreen">"If the forces do not compensate each other, the piston is accelerated in the vertical direction according to the equation of motion," | |||
<div align="center"> | |||
<math>M^*\frac{d^2 h}{dt^2} = -G^* + PA.</math> | |||
</div> | |||
</font> | |||
<br /> <br /> | <br /> <br /> | ||
<br /> <br /> | <br /> <br /> | ||
Revision as of 16:22, 12 March 2026
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 is held in a vertical container with a movable piston resting on top of — and confining — the gas; the mass of the piston is . A vertically directed gravitational acceleration, , acts on the piston, in which case the weight of the piston is given by the expression,
"In the case of hydrostatic equilibrium, the gas pressure adjusts in such a way that the weight per unit area is balanced by the pressure:"
"If the forces do not compensate each other, the piston is accelerated in the vertical direction according to the equation of motion,"
See Also
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