Question

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. $p_{i} \left( \frac{T_{1}T_{2}}{T_{1} +T_{2}}\right) $
• B. $2 p_{i} \left( \frac{T_{1}}{T_{1} +T_{2}}\right) $
• C. $2 p_{i} \left( \frac{ T_{2}}{T_{1} +T_{2}}\right) $
• D. $2 p_{i} \left( \frac{T_{1}T_{2}}{T_{1} +T_{2}}\right) $

Answer 1

Answer: (C)

$n _{1}=\frac{ p _{ i } V }{ RT _{1}} n _{2}=\frac{ p _{ i } V }{ RT _{1}}\,\,\,\,\,\,\,\,$ $\,\,\,\,n _{1}'=\frac{ p _{ f } V }{ RT _{1}}n _{2}'=\frac{ p _{ f } V }{ RT _{2}}$

$n _{1}+ n _{2}= n _{1}'+ n _{2}'$

$\frac{ p _{ i } V }{ RT _{1}}+\frac{ p _{ i } V }{ RT _{1}}=\frac{ p _{ f } V }{ RT _{1}}+\frac{ p _{ f } V }{ RT _{2}}$

$\frac{2 p _{ i } V }{ RT _{1}}=\frac{ p _{ f } V }{ R }\left(\frac{ T _{1}+ T _{2}}{ T _{1} T _{2}}\right)$

$p _{ f }=\frac{2 p _{ i } T _{2}}{ T _{1}+ T _{2}}$