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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.

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To solve the problem, we will use the Paschen equation and the principles of gas laws, particularly Boyle's Law, to show that the sparking potential remains constant as the piston is moved in or out. ### Step-by-step Solution: 1. **Understanding the Setup**: - We have a cylindrical tube closed at one end with a movable piston at the other end. - A cathode is fixed near the closed end, and an anode is attached to the piston. - The tube is filled with gas at pressure \( p \). ...
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