One mole of $O_{2}$ gas having a volume equal to 22.4 litres at $0^{\circ}$ C and 1 atmospheric pressure in compressed isothermally so that its volume reduces to 11.2 litres. The work done in this process is

1672.5 J

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1728 J

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-1728 J

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-1572.5 J

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Solution

The correct option is D -1572.5 J
$W = - μ R T l o g_{e} \frac{V_{2}}{V_{1}} = - 1 \times 8.31 \times (273 + 0) l o g_{e} (\frac{22.4}{11.2})$

$= - 8.31 \times 273 \times l o g_{e} 2 = - 1572.5 J [∴ l o g_{e} 2 = 0.693]$

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One mole of O2 gas having a volume equal to 22.4 litres at 0∘ C and 1 atmospheric pressure in compressed isothermally so that its volume reduces to 11.2 litres. The work done in this process is

The correct option is D -1572.5 JW=−μRTloge V2V1=−1×8.31×(273+0)loge(22.411.2) =−8.31×273×loge2=−1572.5J [∴loge 2=0.693]

One mole of $O_{2}$ gas having a volume equal to 22.4 litres at $0^{\circ}$ C and 1 atmospheric pressure in compressed isothermally so that its volume reduces to 11.2 litres. The work done in this process is

The correct option is D -1572.5 J
$W = - μ R T l o g_{e} \frac{V_{2}}{V_{1}} = - 1 \times 8.31 \times (273 + 0) l o g_{e} (\frac{22.4}{11.2})$

$= - 8.31 \times 273 \times l o g_{e} 2 = - 1572.5 J [∴ l o g_{e} 2 = 0.693]$