NEET · Physics · STD 11 - 12 . kinetic theory of gases

A container has two chambers of volumes \(V_1=2\) litres and \(V_2=3\) litres separated by a partition made of a thermal insulator. The chambers contains \(n_1=5\) and \(n_2=4\) moles of ideal gas at pressures \(p_1=1 atm\) and \(p_2=2 atm\), respectively. When the partition is removed, the mixture attains an equilibrium pressure of:

A 1.3 atm
B 1.6 atm
C 1.4 atm
D 1.8 atm

Verified Solution

Answer & Solution

Correct Answer

(B) 1.6 atm

Step-by-step Solution

Detailed explanation

By energy conservation
\(E _1+ E _2= E _{\operatorname{mix}} \)
\( \frac{n _1 f _1 RT _1}{2}+\frac{n _2 f _2 RT _2}{2}=\frac{\left( n _1 \times n _2\right) fRT _{\operatorname{mix}}}{2} \)
\( \Rightarrow \frac{3}{2} P _1 V_1+\frac{3}{2} P _2 V_2=\frac{3}{2} P _{\operatorname{mix}}\left( V _1+ V _2\right) \)
\( \frac{3}{2} \times 1 \times 2+\frac{3}{2} \times 2 \times 3=\frac{3}{2} \times P _{\operatorname{mix}}(5) \)
\( \therefore P _{\operatorname{mix}}=\frac{8}{5} \)
\( P _{\operatorname{mix}}=1.6 atm\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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