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Consider a cylindrical tube closed at on...

Consider a cylindrical tube closed at one end and fitted with a conducting, movable piston at the other end. A cathode is fixed in the tube near the closed end and an anode is fixed with the piston. A gas is filled in the tube at pressure `p`. Using Paschen equation `V = f(pd), show that the sparking potential does not change as the piston is slowly moved in or out. Assume that the temperature does not change in the process.

Text Solution

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As the piston is moved, the volume of the gas and hence its pressure changes. As the tube is cylindrical, the volume is proportional to the length of the tube. From Boyle's law, `pd = constant` and hence the sparking potential does not change as the piston is moved.
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