Two moles of ideal monoatomic gas was taken through isochoric heating from 100 K to 800 K. If the process is carried out irreversibly (one step) then $Δ S_{s y s t e m} + Δ S_{s u r r o u n d i n g}$ is

[Given : $l n 2 = 0.7$ and $R = 2 c a l / m o l K$ ]

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3.675 cal/K

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7.35 cal/K

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None of these

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Solution

The correct option is C 7.35 cal/K
$Δ S_{s y s t e m} = n C_{v, m} l n (\frac{T_{2}}{T_{1}}) \Rightarrow 2 \times \frac{3}{2} R l n (\frac{800}{100})$

$Δ S_{s y s t e m} = 3 R l n 8 = 12.6 c a l / K$

Entropy of surrounding = $- q / T$
$q = n C_{v} Δ T$

$Δ S_{s u r r o u n d i n g} = - \frac{2 \times \frac{3}{2} R \times 700}{800} \Rightarrow - 2.625 R$

$\Rightarrow - 5.25 c a l / K$

$Δ S_{t o t a l} = 7.35 c a l / K$

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Similar questions

Two moles of ideal monoatomic gas was taken through isochoric heating from 100 K to 800 K. If the process is carried out irreversibly (one step) then $Δ S_{s y s t e m} + Δ S_{s u r r o u n d i n g}$ is

[Given : $l n 2 = 0.7$ and $R = 2 c a l / m o l K$ ]

Q. One mole of ideal monoatomic gas was taken through reversible isochoric heating from 100 K to 1000 K. Calculate

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Pressure of 10 moles of an ideal gas is changed from 2 atm to 1 atm against constant external pressure without change in temperature. If surrounding temperature (300 K) and pressure (1 atm) always remains constant then calculate total entropy change ( $Δ S_{s y s t e m} + Δ S_{s u r r o u n d i n g})$ for given process. [Given: ℓn2 = 0.70 amd R=8.0 J/mol/K]

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Two moles of ideal monoatomic gas was taken through isochoric heating from 100 K to 800 K. If the process is carried out irreversibly (one step) then ΔSsystem + ΔSsurrounding is [Given : ln 2 = 0.7 and R = 2 cal/mol K]

The correct option is C 7.35 cal/KΔSsystem = nCv,m ln(T2T1) ⇒ 2 × 32 R ln(800100) ΔSsystem = 3R ln 8 = 12.6 cal/K Entropy of surrounding = −q/T q=nCvΔT ΔSsurrounding = −2 × 32R × 700800 ⇒ −2.625 R ⇒ −5.25 cal/K ΔStotal = 7.35 cal/K

Two moles of ideal monoatomic gas was taken through isochoric heating from 100 K to 800 K. If the process is carried out irreversibly (one step) then $Δ S_{s y s t e m} + Δ S_{s u r r o u n d i n g}$ is

[Given : $l n 2 = 0.7$ and $R = 2 c a l / m o l K$ ]