How many kinds of plants are there?

Explanation

Consider an ideal gas enclosed in a cylinder is fitted with a weightless and frictionless piston. Now the work is done when gas filled in cylinder expands or contracts against external pressure. Let external pressure acting on system = P
Area of corss section of pison = A
Intially, volume of gas in cylinder = (a) = `V_(1)`
Volume of gas in cylinder (b) = `V_(2)`
If the gas filled in cylinder .a. exerts less pressure than the external pressure then, the piston starts moving down till the internal pressure becomes equal to exteranal pressure. During compression, the piston will move through a small distane dl. Then, volume change `dV = A xx dl`

We know that,
`Pressure = ("Force")/("Area") = P = (F)/(A) or F = p xx A`
Now as the piston moves down through a small distance = dl
Therefore, small work done on system = dl
dw = `dw = "force" xx "distance" = F xx dl`
By putting the value of force (F) from equation (i) into (ii), we have
`dw = p xx A xx dl`
`dw = p.dV [therefre dV = A xx dl]`
If system expands by finite volume, `V_(1) to V_(2)` during compression, then the total work done will come out by integrating eqution (iii).
`W = int dw = p int_(V_(1))^(v_(2)) dV`
`W = p(V_(2) - V_(1))` or W = `p Delta V`, where `Delta V = V_(2) - V_(1)`,
The work done on system may be expressed as follows :