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Two moles of an ideal gas undergo free expansion from 10 L to 100 L at 300 K. The values of ΔSSystem and ΔSSurroundings are (R is universal gas constant)
A
ΔSSystem = 0; ΔSSurroundings = 0
B
ΔSSystem = 4.606R; ΔSSurroundings = −4.606R
C
ΔSSystem = 0; ΔSSurroundings = 4.606 R
D
ΔSSystem = 4.606R; ΔSSurroundings = 0
Explanation
It is isothermal free expansion from 10 lt to 100lt at 300 K, 2 mole gas is taken. ΔSsys = nRℓn(V₂/V₁) = 2Rℓn(100/10) = 2Rℓn10 = 2R × 2.303 = +4.606R as dT = 0, ΔU = 0 Pext = 0 (as free expansion) WPV = 0 First law ΔU = Q + W 0 = Q + 0 Q = 0 As no heat is exchanged between system and surrounding ΔSsurr. = −Qsys/T ΔSsurr. = 0
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