Derive Boyle.s formula according to his law.

Explanation

This Isothermal curve is according to high temperature.
Boyle.s law : ..At constant temperature, the pressure of a fixed amount (i.e., number of moles n) of gas varies inversely with its volume..
Mathematically, it can be written as
`p prop (1)/(V)` (at constant T and n) .....(Eq. -i)
`therefore p = k_(1)(1)/(V)` .....(Eq.-ii)
where, `k_(1)=` Proportionality constant, its value depends upon the amount of the gas temperature of the gas and the units in which p and V are expressed.
`pV=k_(1)` (at constant T and n) .....(Eq. -iii)
Derivation of `p_(1)V_(1)=p_(2)V_(2)` : Suppose fixed amount of gas at constant temperature (T) occupying volume `V_(1)` at pressure `p_(1)` undergoes expansion , so that volume becomes `V_(2)` and pressure becomes `p_(2)`.
According to Boyle.s law at constant T and n, then `p_(1)V_(1)=k_(1)` and `p_(2)V_(2)=k_(1)`
`therefore p_(1)V_(1)=p_(2)V_(2)=` constant ......(Eq. -iv)
`therefore (p_(1))/(p_(2))=(V_(2))/(V_(1))` .....(Eq. -v)