An air$-$standard dual cycle has a compression ratio of $20$ and a cutoff ratio of $1\mathrm{.}100.$ The pressure ratio during the constant$-$volume heat addition process is $1\mathrm{.}2.$ This cycle is operated at $14$ psia and $70$F at the beginning of the compression. Calculate the exergy that is lost each time the cycle is repeated. The surroundings are at $14\mathrm{.}7$ psia and $70$F$.$ The source temperature is the same as the maximum cycle temperature, and the sink temperature is the same as the minimum cycle temperature. Use constant specific heats at room temperature. The properties of air at room temperature are R$=0\mathrm{.}3704$psia$$ft$3/$lbm$$R$,$cp$=0\mathrm{.}240$Btu$/$lbm$$R$,$cv$=0\mathrm{.}171$Btu$/$lbm$$RR$=0\mathrm{.}3704$psia$$ft$3/$lbm$$R$,$cp$=0\mathrm{.}240$Btu$/$lbm$$R$,$cv$=0\mathrm{.}171$Btu$/$lbm$$R $,$ and k $=1\mathrm{.}4.$

The exergy that is lost each time the cycle is repeated is Btu$/$lbm$.$