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Standard XII

Chemistry

PV Work

One mole of a...

Question

One mole of an ideal gas is taken from a to b along two paths denoted by the solid and dashed line as shown in the graph above. If the work done along the solid line path is $w_{s}$ and that along the dotted line path is $w_{d}$ , then the integer closest to the ratio $w_{d} / w_{s}$ is:

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Solution

Work under = Area under the P.V curve:

$W_{s} = \frac{1}{2} \times (4 + 2) \times 1 + \frac{1}{2} \times (2 + 1) \times \frac{3}{2} + \frac{1}{2} \times (1 + 0) \times 3$

$= 3 + \frac{9}{4} + \frac{3}{2} = 6.75$

$W_{d} = 4 \times 3 + 1 \times 2.5 = 14.5$

$∴ \frac{w_{d}}{w_{s}} = \frac{14.5}{6.75} = 2.14$

$∴$ Closest integer $= 2$

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One mole of an ideal gas is taken from a to b along two paths denoted by the solid and dashed line as shown in the graph above. If the work done along the solid line path is ws and that along the dotted line path is wd, then the integer closest to the ratio wd/ws is:

Work under = Area under the P.V curve:Ws=12×(4+2)×1+12×(2+1)×32+12×(1+0)×3 =3+94+32=6.75 Wd=4×3+1×2.5=14.5∴wdws=14.56.75=2.14∴ Closest integer =2

One mole of an ideal gas is taken from a to b along two paths denoted by the solid and dashed line as shown in the graph above. If the work done along the solid line path is $w_{s}$ and that along the dotted line path is $w_{d}$ , then the integer closest to the ratio $w_{d} / w_{s}$ is: