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Derivean expressionfor theworkdoneduringthe isothermalexpansionof an ideal gas. |
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Answer» Solution :Considern molesof an idealgascontainedin acylinderhavingconductingwallsandprovidedwithfrictionless andmovablcpiston. P - pressureofthe gas , A - areaof thepiston , dV-smallincreasesin thevolumeof thegas Workdoneby the gaswhenthepiston movesup THROUGHA smalldistance DW = PA DX. = Pd V Supposethe gasexpandsisothermallyfrom `P_(1)V_(1)` to `P_(2) V_(2)` The totalamountworkdone `W_("iso" ) =UNDERSET( V_(1))overset( V_(2)) PdV` FornmolesPV= nRT(or )`P = (n Rt)/( V)` `W _("iso") = underset(V_(1))overset(V_(2))(int)(n RT)/(V ).dV= n Rtunderset(V_(1))overset(V_(2))(int).(1)/(V).dV` `n Rt[ logV ] _(V_(1))^(V_(2))= nRt [ logV_(2)- log_(e ) V_(1)^(t) ]` `W _("iso") = nRt["log".(V_(2))/(V_(1))]= 2.303nRt"log" .((V_(2))/(V_(1)))` `= 2.303n Rtlog .((P_(1))/(P_(2)))` |
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