One mol an ideal gas is expanded from`(10 atm, 10lit)`. `(2 atm , 50 lit)` isothermally . First against 5 atm then against 2 atm . Calculate work done

Monjur Alahi

One mol an ideal gas is expanded from`(10 atm, 10lit)`. `(2 atm , 50 lit)` isothermally . First against 5 atm
then against 2 atm . Calculate work done in each step and compare it with single step work done.


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Salim Ahmed Kawsar

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`P_(1)" "V_(2) " "overset(Isothermal)to" "P_(1)" "V_(1)`
10 atm 10 lit `" "`2 atm 50 lit.
(i) Work done against 5 atm pressure `(underset("10 atm")(P_(1))" "underset("10 lit")(V_(1)) to underset("5 atm ")(P_(2))underset(" 20 lit")" "V_(2))`
Vol. of system at 5 atm `=(10 xx 10)/(5)= 20 lit`.
`W_("irrev") = - P_("ext") (V_(2)- V_(1)) = - 5(20-10) =- 50 "atm lit"`
(ii) Work done agnist 2 atm
`underset("5 atm") (P_(1))" "underset("20 lit")(V_(1))to underset("2 atm") (P_(2))" "underset("50 lit")(V_(2))`
`W_("irr")= - P_("ext") (V_(2)- V_(1)) = - 2xx (50-20)= - 60 " atm lit"`
`W_("total")= - 50- 60 = - 110" atm lit"`
Total work done aganist 2 atm
`underset("10 atm") (P_(1))" "underset("10 lit")(V_(1))to underset("2 atm") (P_(2))" "underset("50 lit")(V_(2))`
`W = - 2(50-10) = - 80" atm lit"`.
Magntiude of work done in more than one step is more than single step work done.

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