Move the piston, you don't want it to burn

Classical Mechanics Level 5

A resistor of resistance \(R = 500 \Omega\) connected to an external battery is placed inside a cylinder fitted with a friction-less piston of mass \(M=10\text{ kg}\), area of cross section \(10^{-3} \text{ m}^2\) and contains \(2\) moles of an ideal mono-atomic gas. A current \(i = 0.3 A\) flows through the resistance.

The temperature of the gas is maintained constant by moving the piston with a velocity \(v\) upward (measured in \(\text{m/s}\)).

What is the value of \( \lfloor 1000v \rfloor \)?

Details and Assumptions

  • The cylinder is thermally insulated.
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