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A cycle followed by an engine (made of one mole of an ideal gas in a cyclinder with a piston) is shown in (figure). Find heat exchanged by the engine, with the surrounding for each section of the cycle. `[C_(V)= (3//2)R]`
AB : constant volume BC : constant pressure
CD : adiabatic DA : constant pressure.

Text Solution

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(i) In (figure), Portion AB of the cycle involves increase in pressure/temp. of gas at constant volume. Therefore, the system gains heat from the surroundings,
`Q_(AB)=U_(AB)=3/2R(T_(B)-T_(A))= 3/2(P_(B)V_(B)-P_(A)V_(A))=3/2(P_(B)-P_(A))V_(A)`
(ii) In the portion BC, the gas increase in volume at constant pressure. Heat required for this is gained from surroundings
`Q_(BC)=U_(BC)+W_(BC)=3/2(P_(C)V_(C)-P_(B)V_(B))+P_(B)(V_(C)-V_(B))=5/2P_(B)(V_(C)-V_(B)) ( :. P_(C)=P_(B))`
`Q_(BC)= 5/2P_(B)(V_(C)-V_(A))`
(iii) As `CD` represents an adiabatic change, therefore, `Q_(CD)=0`
(iv) `DA` involves compression of gas from `V_(D) "to" V_(A)` at constant pressure `P_(A)`. Work is done on the gas.
`Q_(DA)=(-5)/2P_(A)(V_(D)-V_(A))=5/2P_(A)(V_(A)-V_(D))`
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