In a certain thermodynamic process, pressure is a parabolic function of volume with the function having its minima at P=5 bar and `V=5dm^(3)`. If anideal gas undergoes this process and in due course its volume is increased from `4dm^(3)` to `10dm^(3)`, then the work done in the process is ________kJ(1 bar =`10^(5)` Pa)

Answer

`07.20`

Explanation

The standard equation of a parabola with minima at (h,k) is given as `(y-k)=(x-h)^(2)`. Thus for given parabola, equation can be given as
`(P-k)=(V-h)^(2)`
`:.(P-5)=(V-5)^(2)`
`:.(P-5)=V^(2)-10V+25`
`:.P=V^(2)-10V+30`
now `dW=PdV`
`:.W=int_(4)^(10)(V^(2)-o10V+30)dV`
`W=[(V^(3))/3]_(4)^(10)-10[(V^(2))/2]_(4)^(10)+30[V]_(4)^(10)`
`=((1000-64)/3)-10((100-16)/2)`
`+30(10-4)`
`=312-420+180`
`=72bardm^(3)`
`=72xx10^(5)xx10^(-3)J`
`:.W=7.2kJ`