Two chambers, one containing `m_(1)`g of a gas at `P_(1)` pressure and other containing `m_(1)`g of a gas at `P_(2)` pressure are put in communication with each other. If temperature remains constant, the common pressure reached will be

Explanation

According to Boyle.s law `(P)/(rho)` = cons tan t
`therefore V_(1) = (m_(1))/(P_(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`.
`rho = ((m_(1) + m_(2)))/(k ((m_(1))/(P_(1)) + (m_(2))/(P_(2)) ) ) rArr P = k rho = ( (m_(1) + m_(2))/((m_(1))/(P_(1)) + (m_(2))/(P_(2)) ))t = (P_(1) P_(2) (m_(1) + m_(2)) )/((P_(2) m_(1) + m_(2) P_(1) ) ) `