Two chambers, one containing `m_(1)g` of gas at `P_(1)` pressure and other containing `m_(2)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` = constant
`thereforeV_(1)=m_(1)/rho_(1)=(km_(1))/P_(1)andV_(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)))`
`rArrP=krho=((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)))`