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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 Pf is

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
Initially, number of moles of gas in each bulb is
`n_(1)=(P_(i)V)/(RT_(1))` and `n_(2)=(P_(i)V)/(RT_(1))`
After the temperature of second bulb is raised to `T_(2)` then the number of moles of gas in both the bulbs are
`n'_(1)=(P_(f)V)/(RT_(1))` and `n'_(2)=(P_(f)V)/(RT_(2))`
Now, the total number of moles of gas in both the bulbs
remains same in both the cases.
`n_(1)+n_(2)=n'_(1)+n'_(2)`
`(2p_(i)V)/(RT_(1))=(p_(f)V)/(RT_(1))+(p_(f)V)/(RT_(2)) rArr (2p_(i)V)/(RT_(1))=(p_(f)V)/(R )((T_(2)+T_(1))/(T_(1)T_(2)))`
`p_(f)=(2p_(i)T_(2))/(T_(1)+T_(2))`
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