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Air is initially at 260^(@)C and 700pa a...

Air is initially at `260^(@)C` and `700pa` and occupied `0.028m^(3)`. The air is expanded at constant pressure to `0.084 m^(3)`. A polytropic process with `n=1.5` is then carried out followed by a constant temperature process which complete the cycle.
`(a)` sketch cycle in `P-V`.
`(b)` find heat received and heat rejected in the cycle.
`(c )` efficiency of cycle.

Text Solution

Verified by Experts

`P_(1)=700Pa`,`V_(2)=0.08m^(3)`
`P_(1)V_(1)=nRT_(1)`
No.of moles `v=(700xx0.028)/(8.31xx533)=0.004"mole"`
`(T_(2))/(T_(1))=(V_(2))/(V_(1))=3`
`T_(2)=3T_(1)=1599K`
`PV^(n)=C`
`P((nRT)/(P))^(n)=C`
`rArrP=C'T^((n)/(n-1))`
`(P_(2))/(P_(3))=((1599)/(533))^(1.5//0.5)=3^(3)=27`.
`Q_(1-2)=vC_(p)(T_(2)-T_(1))=0.004xx(7)/(2)xx8.31(1599-533)=124J`.
`Q_(2-3)=DeltaU+intPdV`
`=vC_(v)(T_(3)-T_(2))+(nR(T_(2)-T_(3)))/(n-1)=vC_(v)((n-gamma)/(n-1))(T_(3)-T_(2))`
`=0.004xx(5)/(2)xx8.31(0.1)/(0.5)(-1066)=-17.7J`.
`Q_(31)=W_(31)=vRT_(1)ln((V_(1))/(V_(3)))=0.004xx8.31xx533ln((P_(3))/(P_(1)))=-58.4J`
`(SigmaQ)_("cycle")=(Sigmaw)_("cycle")`
`SigmaW=Q_(1-2)+Q_(2-3)+Q_(3-1)=124-17.7-58.4=47.9J`.
`eta_("cycle")=(W_("net"))/("Heat supplied")=(47.9)/(106)xx100=38.6%`
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