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A closed tank has two compartments A and B, both filled with o

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A closed tank has two compartments $A$ and $B$ , both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (first figure). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (second figure), the volume (in $m^{3}$ ) of the compartment $A$ after the system attains equilibrium is

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Updated on: May 15, 2023

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New Pattern JEE Problems Chemistry for JEE Main and Advance( Master Problem Package) (Arihant)

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A closed tank has two compartments

A

and

B

, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (first figure). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (second figure), the volume (in

m^{3}

) of the compartment

A

after the system attains equilibrium is

12 mins ago

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12 mins ago

Text solutionVerified

(2.22) Given,

p_{1} = 5 bar, V_{1} = 1 m^{3}, T_{1} = 400 K

So,

, n_{1} = \frac{5}{400 R} (

from

p V = n RT)

Similarly,

p_{2} = 1

bar,

V_{2} = 3 m^{3}, T_{2} = 300 K

n_{2} = \frac{3}{300 R}

Let at equilibrium the new volume of

A

will be

(1 + x)

So, the new volume of

B

will be

(3 - x)

Now, from the ideal gas equation.

\frac{p _{1} V _{1}}{n _{1} R T _{1}} = \frac{p _{2} V _{2}}{n _{2} R T _{2}}

and at equilibrium (due to conduction of heat)

\frac{p _{1}}{T _{1}} = \frac{p _{2}}{T _{2}}

So,

\frac{V _{1}}{n _{1}} = \frac{V _{2}}{n _{2}}

V_{1} n_{2} = V_{2} n_{1}

After putting the values

(1 + x) \times \frac{3}{300 R} = (3 - x) \times \frac{5}{400 R}

(1 + x) = \frac{( 3 - x ) 5}{4}

4 (1 + x) = 15 - 5 x

4 + 4 x = 15 - 5 x

x = \frac{11}{9}

Hence, new volume of

A

i.e.,

(1 + x)

will comes as

1 + \frac{11}{9} = \frac{20}{9}

2.22

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Question Text	A closed tank has two compartments $A$ and $B$ , both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (first figure). If the old partition is replaced by a new partition which can slide and conduct heat but does not allow the gas to leak across (second figure), the volume (in $m^{3}$ ) of the compartment $A$ after the system attains equilibrium is
Updated On	May 15, 2023
Topic	States of Matter
Subject	Chemistry
Class	Class 11
Answer Type	Text solution:1 Video solution: 9
Upvotes	1025
Avg. Video Duration	10 min

Text solutionVerified

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