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Derive Boyle.s formula according to his law. |
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Answer» Solution :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) |
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