Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure pi and temperature T1 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 T2. The final pressure pf is :

Question

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure pi and temperature T1 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 T2. The final pressure pf is : (A) pi ( (T1T2/T1 +T2))  (B) 2 pi ( (T1/T1 +T2))  (C) 2 pi ( ( T2/T1 +T2))  (D) 2 pi ( (T1T2/T1 +T2))

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/chemistry/6be8cc9d05b23f6fe5a15cb102794cc0-.png" /> n 1=( p i V / RT 1) n 2=( p i V / RT 1) n 1'=( p f V / RT 1)n 2'=( p f V / RT 2) n 1+ n 2= n 1'+ n 2' ( p i V / RT 1)+( p i V / RT 1)=( p f V / RT 1)+( p f V / RT 2) (2 p i V / RT 1)=( p f V / R )(( T 1+ T 2/ T 1 T 2)) p f =(2 p i T 2/ T 1+ T 2)

$p_{i} (\frac{T _{1} T _{2}}{T _{1} + T _{2}})$

$2 p_{i} (\frac{T _{1}}{T _{1} + T _{2}})$

$2 p_{i} (\frac{T _{2}}{T _{1} + T _{2}})$

$2 p_{i} (\frac{T _{1} T _{2}}{T _{1} + T _{2}})$

Q. Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure pi​ and temperature T1​ 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 T2​. The final pressure pf​ is :

pi​(T1​+T2​T1​T2​​)

2pi​(T1​+T2​T1​​)

2pi​(T1​+T2​T2​​)

2pi​(T1​+T2​T1​T2​​)

n1​=RT1​pi​V​n2​=RT1​pi​V​ n1′​=RT1​pf​V​n2′​=RT2​pf​V​ n1​+n2​=n1′​+n2′​ RT1​pi​V​+RT1​pi​V​=RT1​pf​V​+RT2​pf​V​ RT1​2pi​V​=Rpf​V​(T1​T2​T1​+T2​​) pf​=T1​+T2​2pi​T2​​

$p_{i} (\frac{T _{1} T _{2}}{T _{1} + T _{2}})$

$2 p_{i} (\frac{T _{1}}{T _{1} + T _{2}})$

$2 p_{i} (\frac{T _{2}}{T _{1} + T _{2}})$

$2 p_{i} (\frac{T _{1} T _{2}}{T _{1} + T _{2}})$