KVPY 2020-21 SB SX Exam Previous Papers

Question : 107 of 120

Marks: +1, -0

A container is divided into two compartments by a removable partition as shown below :

In the first compartment,

n_1

moles of ideal gas He is present in a volume

V_1

. In the second compartment,

n_2

moles of ideal gas Ne is present in a volume

V_2

. The temperature and pressure in both the compartments are T and P, respectively. Assuming R is the gas constant, the total change in entropy upon removing the partition when the gases mix irreversibly is :

${n}_{1} {R} l{n} {{V}_{1}}/{{V}_{1}+{V}_{2}}+{n}_{2} {R} l{n} {{V}_{2}}/{{V}_{1}+{V}_{2}}$
${n}_{1} {R} l{n} {{V}_{1}+{V}_{2}}/{{V}_{1}}+{n}_{2} {R} l{n} {{V}_{1}+{V}_{2}}/{ {V}_{2}}$
$({n}_{1}+{n}_{2}) {R} l{n} {{n}_{1} {V}_{1}}/{{n}_{2} {V}_{2}}$
$({n}_{1}+{n}_{2}) {R} l{n} {{n}_{2} {V}_{2}}/{{n}_{1} {V}_{1}}$

Validate

Solution:

Entropy change

\Δ{S}={nC}_{{v}} l{n}

({{T}_{2}}/{{T}_{1}})+{nR} l{n}({{V}_{2}}/{{V}_{1}})

Since temperature is constant throughout process.

{He}: \Δ{S}={n}_{1} {R} l{n}({{V}_{1}+{V}_{2}}/{{V}_{1}})

{Ne}: \Δ{S}={n}_{2} {R} l{n}({{V}_{1}+{V}_{2}}/{{V}_{2}})

Total change in

(\ΔS)={n}_{1} {R} l{n} {{V}_{1}+{V}_{2}}/{{V}_{1}}+{n}_{2} {R} l{n} {{V}_{1}+{V}_{2}}/{ {V}_{2}}

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