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:

Options

A. `2p,((T_(2))/(T_(1)+T_(2)))`
B. `2p,((T_(1)T_(2))/(T_(1)+T_(2)))`
C. `p,((T_(1)T_(2))/(T_(1)+T_(2)))`
D. `2p,((T_(1))/(T_(1)+T_(2)))`

Answer

A

Explanation

For a given mass ofan ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant. i.e
`Vpropn`
Hence in the given case.
Initial moles and final moles are equal `(n_(T))_(i) =(n_(T))_(f)`
`(P_(1)V)/(RT_(1))+(P_(i)V)/(RT_(1))=(P_(f)V)/(RT_(1))+(P_(f)V)/(RT_(2))`
`2(P_(i))/(T_(1))=(P_(f))/(T_(1))+(P_(f))/(T_(2))`
`P_(f)=(2P_(i)T_(2))/(T_(1)+T_(2))`