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Two closed bulbs of equal volume (V) con...

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure `p_(i)` and temperature `T_(1)` are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to `T_(2)`. The final pressure `p_(f)` is:

A

`2p_(i)((T_(1))/(T_(1)+T_(2)))`

B

`2p_(i) ((T_(1)T_(2))/(T_(1)+T_(2)))`

C

`2p_(i) ((T_(1)T_(2))/(T_(1)+T_(2)))`

D

`p_(i)((T_(1)T_(2))/(T_(1)+T_(2)))`

Text Solution

Verified by Experts

The correct Answer is:
B
Initial moles = final moles
`(P_(i)xxV)/(RT_(1)) +(P_(i)xxV)/(RT_(1)) =(P_(f)xxV)/(RT_(2)) +(P_(f)xxV)/(RT_(1))`
`(P_(i))/(T_(1))+(P_(i))/(T_(1)) =(P_(f))/(T_(2))+(P_(f))/(T_(1))`
`(2P_(i))/(T_(1))=P_(f)[1/(T_(2))+1/(T_(1))]`
`(2P_(i))/(T_(1))=P_(f) [(T_(1)+T_(2))/(T_(1)T_(2))]`
`P_(f) = 2P_(i) xx ((T_(2))/(T_(1)+T_(2)))`
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