1.

A gas (gamma=1.5) undergoes a cycle of adiabatic, isobaric and isochoric processes in an order. If the volume of the gas is doubled in the adiabatic process then the efficiency of the cycle is approximately,

Answer»

`18%`
`46.4%`
`38.5%`
`9.25%`

Solution :According to the question, we drawn the FOLLOWING situation,
In isochoric process, `(p_(A))/T_(A)=p_(B)/T_(B)`

As work done in ADIABATIC process,
`W=(nR(T_(1)-T_(2)))/(y-1)=(R(T-T/sqrt(2)))/((1.5-1)) ""("Taking, " n=1)`
`V_(2)=2V_(1)`
`rArr ""T_(2)=T_(1)/sqrt(2) " or "T_(2)=T/sqrt(2)`
`W_(t)=RT 2(1-1/sqrt(2))=0.58 ""(because r=i " Given ")`
Work done in isobaric process,
`""W_(2)=pDeltaV=nRDeltaT`
`rArr W=nR(T/(2sqrt(2))-T/sqrt(2))=-RT(1/sqrt(2)-1/(2sqrt(2)))=-0.35`
Now, heat given to system
`Q_(1)=nC_(p)DeltaT=7/2R(1/sqrt(2)-1/(2sqrt(2)))=-1.23 J`
Negative, `Q_(1)` shows that heat is given to the system.
Efficiency of the CYCLE,
`""eta="net work done"/"heat input"=(W_(1)+W_(2))/Q_(1)`
`""=(0.58-0.35)/1.23`
`rArr ""eta=0.23/1.23 TIMES 100 =18.6%=18%`
Hence, the efficiency of cycle is 18%.


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