Question

Show by direct substitution for vf and vi that the ideal gas law implies PΔV = vRΔT when P and V are constant, where ΔV = Vf-Vi and ΔT = Tf −Ti

Answer 1

Solution:

Ideal gas equation , PV = vRT ...............................................(1)

where P = pressure , V = volume , v= no of moles , R = Universal gas constant , T= absolute temperature

now for process i equation 1 can be written using subscript i as follows

PVi= vRTi .........................................................(2)

P and v are constant .

and for process f equation 1 can be written using subscript f as follows

PVf= vRTf ........................................................(3)

P and v are constant.

now subtracting equation 3 from equation 2 we get

PVf - PVi = vRTf  - vRTi

or, P ( Vf  - Vi ) = vR(Tf  - Ti)

or, PV = vRT ; where V = ( Vf  - Vi ) and T=(Tf  - Ti)

So , PV = vRT ( proved )

Thank You.