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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Chemistry
Chapter
States of Matter

NTA Abhyas 2020 · Chemistry · States of Matter

Two closed bulbs of equal volume (V) containing an ideal gas...

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure pi{p}_{i} and temperature T1{T}_{1} are connected through a narrow tube negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to T2{T}_{2}. The final pressure pf{p}_{f}

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure p _ i and temperature T _ 1 are

Options

  1. A2pi(T1T2T1+T2)2{p}_{i} \left(\dfrac{{T}_{1}{T}_{2}}{{T}_{1} + {T}_{2}}\right)
  2. Bpi(T1T2T1+T2){p}_{i} \left(\dfrac{{T}_{1}{T}_{2}}{{T}_{1} + {T}_{2}}\right)
  3. C2pi(T1T1+T2)2{p}_{i} \left(\dfrac{{T}_{1}}{{T}_{1} + {T}_{2}}\right)
  4. D2pi(T2T1+T2)2{p}_{i} \left(\dfrac{{T}_{2}}{{T}_{1} + {T}_{2}}\right)

Correct answer

D. 2pi(T2T1+T2)2{p}_{i} \left(\dfrac{{T}_{2}}{{T}_{1} + {T}_{2}}\right)

Step-by-step solution

Initial moles and final moles are equal

(nT){\left({n}_{T}\right)}_{i} = {\left({n}_{T}\right)}_{f}

P1VRT1+P1VRT1=PfVRT1+PfVRT2\dfrac{{P}_{1}V}{R{T}_{1}} + \dfrac{{P}_{1}V}{R{T}_{1}} = \dfrac{{P}_{f}V}{R{T}_{1}} + \dfrac{{P}_{f}V}{R{T}_{2}}

2PiT1=PfT1+PfT22\dfrac{{P}_{i}}{{T}_{1}} = \dfrac{{P}_{f}}{{T}_{1}} + \dfrac{{P}_{f}}{{T}_{2}}

Pf=2PiT2T1+T2{P}_{f} = \dfrac{2{P}_{i}{T}_{2}}{{T}_{1} + {T}_{2}}
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