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Two cylinder having m(1)g and m(2)g of ...

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

A

`(P_(1)P_(2)(m_(1)+m_(2)))/(P_(1)m_(2)+P_(2)m_(1))`

B

`(m_(1)m_(2)(P_(1)+P_(2)))/(P_(1)m_(2)+P_(2)m_(1))`

C

`(P_(1)P_(2)m_(1))/(P_(1)m_(2)+P_(2)m_(1))`

D

`(m_(1)m_(2)P_(2))/(P_(1)m_(2)+P_(2)m_(1))`

Text Solution

Verified by Experts

The correct Answer is:
A
From Boyle's law, `(P)/(rho)=Const=K`
`rho_(1)=(R_(1))/(K)`, (or) `V_(1)=(m_(1))/(rho_(1))=(m_(1)K)/(P_(1))`
`II^(ly), V_(2)=(m_(2)K)/(P_(2))`
`V=V_(1)+V_(2)=K[(m_(1))/(P_(1))+(m_(2))/(P_(2))], rho=(m_(1)+m_(2))/(v_(1)+v_(2))`
`P=K rho=(P_(1)P_(2)(m_(1)+m_(2)))/(P_(1)m_(2)+P_(2)m_(1))`
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