QJEEM16Ch895c: JEE Main 2016 Chemistry - Class 11 JEEM16Ch895c Solution: Two closed bulbs of equal volume containing an ideal gas…

Question

Verified Solution • 2025–26 Session moderate

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 :

Accepted Answer

For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant.

i.e

V \propto n

Hence in the given case.

Initial moles and final moles are equal

{\left( {{n_T}} \right)_i} = {\left( {{n_T}} \right)_f}

{{{P_i}V} \over {R{T_1}}} + {{{P_i}V} \over {R{T_1}}}

= {{{P_f}V} \over {R{T_1}}} + {{{P_f}V} \over {R{T_2}}}

2{{{P_i}} \over {{T_1}}} = {{{P_f}} \over {{T_1}}} + {{{P_f}} \over {{T_2}}}

\Rightarrow {P_f} = {{2\,{P_i}{T_2}} \over {{T_1} + {T_2}}}

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