Two cylinder having `m_(1)g` and `m_(2)g` of a gas at pressure `P_(1)` and `P_(2)` respectively are put in cummunication with each other, temperature remaining constant. The common pressure reached will be

Explanation

According to Boyle's law `P/(.)` = const.
`:. V_(1) = (m_(1))/(._(1)) = (km_(1))/(P_(1))` and `V_(2) = (km_(2))/(P_(2))`
Total volume `= k (m_(1)/(P_(1)) + m_(2)/(P_(2)))`
Let mixture has common pressure `P` and common density `rho`.
`. = ((m_(1) + m_(2)))/(K((m_(1))/(P_(1)) + m_(2)/(P_(2))))`
`rArr P = k^(*) = (m_(1) + m_(2))/(((m_(1))/(P_(1)) + m_(2)/(P_(2)))) = (P_(1)P_(2)(m_(1) + m_(2)))/((P_(2)m_(1) + m_(2)P_(1)))`