Given that P & V increase in direct proportion such that
When P= 1 atm, V= 1L; P=3 atm, V=3L
Describe a possible setup for the pressure to rise as the volume increases.
The Attempt at a Solution
Suppose a system of
1. a cylinder with volume V, height x and radius r
2. with piston with area A and radius r on top
3. and spring with spring constant k on top the piston
Since pressure acts similarly in all directions, assume that the pressure P acts on A such that
(-kx)/A = P
ΔV= 2pi.r.Δx → Δx= ΔV/(2pi.r) ---->(1)
kΔx/A= ΔP, where A= pi.r2 ---->(2)
Therefore substitute (1) into (2) for Δx, spring constant k is selected such that it fulfills
k = 2pi2.r3. ΔP/ΔV
The basic idea is that Fspring/A = P and at the same time it also fulfills -1/2kx2= Wvolume,pressure for when both equations uses the same P and V.
I have thought of the compression of air but chose to make it negligible. The idea led from me considering that an increase in pressure when volume is increasing must come from a form of suppression/resistance.
However, it is also to be noted that the main source of energy input would be from heat energy, Q.
Would this make sense? Thanks for reviewing.