A mixture of ideal gas containing $$5$$ moles of monatomic gas and $$1$$ mole of rigid diatomic gas is initially at pressure $$P0$$, volume $$V0$$, and temperature $$T0$$. If the gas mixture is adiabatically compressed to a volume $$V0/4$$, then the correct $$statement(s)$$ $$is/are$$, (Given$$ $$21.2$$ $$=$$ $$2.3$$ ; $$23.2$$ $$=$$ $$9.2$$ ; R is gas $$constant)

Question

A mixture of ideal gas containing $$5$$ moles of monatomic gas and $$1$$ mole of rigid diatomic gas is initially at pressure $$P0$$, volume $$V0$$, and temperature $$T0$$. If the gas mixture is adiabatically compressed to a volume $$V0/4$$, then the correct $$statement(s)$$ $$is/are$$, (Given$$ $$21.2$$ $$=$$ $$2.3$$ ; $$23.2$$ $$=$$ $$9.2$$ ; R is gas $$constant)

Infinity Learn · Accepted Answer

$$P1=5RToVoP2=RT0VP1+P2=Po=6RT0V0Ymixture$$ $$=5CP1+(1)CP25CV1+(1)CV2=5$$×$$5R2+(1)7R25$$×$$3R2+(1)5R2=3220=1.6PV$$γ$$=$$ constant ⇒$$P0V01.6=PV0/41.6$$⇒$$P=P0(4)1.6=Po23.2$$⇒$$P=9.2P0$$ Work $$=W=P2V2$$−$$P1V11$$−γ$$=9.2P0V04$$−$$P0V01$$−$$1.6=(2.3$$−$$1)PoV0$$−$$0.6=1.3$$×$$6RT0$$−$$0.6$$⇒$$W=$$−$$13RT0$$⇒|W|$$=13RT0TV$$γ−$$1=$$ constant ⇒TiViγ−$$1=TfVf$$γ−$$1$$⇒$$T0V00.6=TfV040.6$$⇒$$Tf=(2)1.2T0=2.3T0$$ Kinetic Energy $$=nCVmixTf=(6)R1.6$$−$$12.3T0=23RT0$$

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