Answer

Verified

437.1k+ views

**Hint:**First find the equation for how many moles are transferred and then find the equation for volume. Then put these two in the initial equations.

**Complete step by step answer:**Let’s start with understanding the question and for understanding the questions we need to analyse all the given parameters. We are given that

Initial pressure and temperature of two closed vessels is equal and is $P_1$ and $T_1$ respectively. The two vessels are connected with narrow open tubes. The final temperature of vessel A and B is $T_1$ and $T_2$ respectively with $T_1$>$T_2$. Since both the vessels are connected then the final pressure in both the vessels will be the same. Let the final pressure be P.

Let’s assume that x amount of mole is transferred from A to B, now applying the Ideal gas equation we get,

${{{P}}_2}{{{V}}_{}}{{ = (n - x)R}}{{{T}}_{{1}}}$ for vessel A and ${{{P}}_2}{{{V}}_{}}{{ = (n + x)R}}{{{T}}_2}$

This gives (n - x) R$T_1$ = (n + x) R$T_2$

x = $\dfrac{{{{n(}}{{{T}}_{{1}}}{{ - }}{{{T}}_{{2}}}{{)}}}}{{{{{T}}_{{1}}}{{ + }}{{{T}}_{{2}}}}}$

Considering the initial temperature, volume and pressure we will get that

$P_1$ X 2V = 2nR$T_1$ => V = $\dfrac{{{{nR}}{{{T}}_1}}}{{{{{P}}_1}}}$

Putting the value of V and x in ${{{P}}_2}{{{V}}_{}}{{ = (n - x)R}}{{{T}}_{{1}}}$ we get,

\[P_A \times \dfrac nRT_1P_1 = (n - \dfrac n(T_1- T_2T_1 + T_2)RT_1\]

Solving this we will get $P_2$ = \[\dfrac{{{{2}}{{{P}}_{{1}}}{{{T}}_{{2}}}}}{{{{{T}}_{{1}}}{{ + }}{{{T}}_{{2}}}}}\].

**So, the answer to this question is option B.**\[\dfrac{{{{2}}{{{P}}_{{1}}}{{{T}}_{{2}}}}}{{{{{T}}_{{1}}}{{ + }}{{{T}}_{{2}}}}}\].

**Note:**Diffusion is the concept which is largely studied in many fields to get an idea about how different glasses and liquids diffuse into each other. One of the most famous experiments which has been performed by almost everyone is that when you spray the perfume in one corner of the room the smell of the perfume spreads at every corner of the room. This is caused by diffusion of perfume molecules in the air.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Write a letter to the principal requesting him to grant class 10 english CBSE