Question
A particle of mass m in energy state n is confined in an infinite square well potential of width a. A microscopic demon very slowly (adiabatically, as in the particle remains in equal state number n at all times) squeezes the well to half of its width a/2.
How much work that demon will do to accomplish this action?
What is force F (a) required to move the wall as a function of width a.
The analog of pressure on the wall in 1D case is essentially equal to the force a particle imposes on the wall. Write down the expression that shows how that pressure P (a, En) depends on the width of the well and energy of the particle.
Evaluate that expression with the acknowledged gas law for 3D space P ~ T/V, where P is pressure, T is temperature and V is volume. Is there analogy?