One mole of an ideal gas is taken from `a` to `b` along two paths denoted by the solid and the dashed lines as shown in the graph shown. If the work d

Question

One mole of an ideal gas is taken from `a` to `b` along two paths denoted by the solid and the dashed lines as shown in the graph shown. If the work d

One mole of an ideal gas is taken from `a` to `b` along two paths denoted by the solid and the dashed lines as shown in the graph shown. If the work done along the solid line path is `W_(s)` and that along the dotted line path is `W_(d)`, then `W_(d)` integer closest to the ratio `W_(d)//W_(s)`

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - ` to 2`
Horizontal dotted lines indicate the work of constant pressure, each given by `PDeltaV`. Vertical dotted lines indicate that work done is zero because volume remains constant
`W_(d)=(4.0)xx1.5)+(1.0xx1.0)+(0.75xx2.5)L"atm"=6+1+1.815=8.875 L "atm"`
Solid line indicates isothermal reversible expansion. It is isothermal because `PV` is constant
`:. W_(s)=2.303nRT log V_(2)//V_(1)`
`=2.303PVlog V_(2)//V_(1) (PV=nRT)`
`=2.303xx2log"(5.5)/(0.5)(PV=2 L "atm")`
`=4.61 L"atm"`
Hence `=(W_(d))/(W_(s))=(8.875)/(4.61)=2`