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A vessel of volume `V` is evacuated by means of a piston air pump. One piston stroke captures the volume `Delta V`. How many strokes are needed to reduce the pressure in the vessel `eta` times ? The process is assumed to be isothermal, and the gas ideal. |
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Answer» Correct Answer - `n = (In eta)/(In(1+DeltaV//V))` `PV = constant` `PV = P_(1) (V +DeltaV)` `P_(1) = (PV)/(V +DeltaV) ..(1)` `P_(1)V = P_(2)(V +DeltaV)` `P_(2) = (P_(1)V)/(V +DeltaV) ..(2)` from (1) and (2) `P_(2) = P [(V)/(V +DeltaV)]^(2)` similarly `P_(n) = P [(V)/(V + DeltaV)]^(n)` according to problem `(P_(n))/(P) = (1)/(eta)` `(1)/(eta) = ((V)/(V + DeltaV))^(n)` `- ln(eta) = nln ((V)/(V +DeltaV))` `(ln eta)/(n = ln(1+(DeltaV)/(V)))` |
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