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KVPY2020ChemistryThermodynamics (C)

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 w

Options

  1. An 1 Rℓn V 1   V 1 + V 2 + n 2 Rℓn V 2   V 1 + V 2
  2. Bn 1 Rℓn V 1 + V 2   V 1 + n 2 Rℓn V 1 + V 2   V 2
  3. Cn 1 + n 2 Rℓn n 1   V 1 n 2   V 2
  4. Dn 1 + n 2 R ℓn n 2 V 2 n 1 V 1

Correct answer

B. n 1 Rℓn V 1 + V 2   V 1 + n 2 Rℓn V 1 + V 2   V 2

Step-by-step solution

Entropy change ΔS = nC v ℓn T 2   T 1 + nRℓn V 2   V 1 Since temperature is constant throughout process. He : ΔS = n 1 Rℓn V 1 + V 2   V 1 Ne : ΔS = n 2 Rℓn V 1 + V 2   V 2 Total change in ( ΔS ) = n 1 Rℓn V 1 + V 2   V 1 + n 2 R ℓ n V 1 + V 2   V 2

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