hatvolume of vessel = Vinitial pressure = Ptemperature is CONSTANT = Tstroke VOLUME of pump = VWHEN 1st "v" volume is taken out, then the pressure decreases in the vessel.let it becomes P₁. Now, the volume of gas (V-v) at pressure P occupies the whole volume of vessel (V) at pressure P₁. SoP(V-v) = P₁VP₁ = P[(V-v)/V]When 2nd "v" volume is taken out, then the pressure decreases in the vessel.let it becomes P₂. Now, the volume of gas (V-v) at pressure P₁ occupies the whole volume of vessel (V) at pressure P₂. SoP₁(V-v) = P₂VP₂ = P₁ [(V-v) / V]P₂ = [P (V-v) / V] [(V-v) / V]P₂ = P [(V-v) / V]²When 3rd "v" volume is taken out, then the pressure decreases in the vessel.let it becomes P₃. Now, the volume of gas (V-v) at pressure P₂ occupies the whole volume of vessel (V) at pressure P₃. SoP₂(V-v) = P₃VP₃ = P₂ [(V-v) / V]P₃ = P [(V-v) / V]² [(V-v) / V]P₃ = P [(V-v) / V]³So final pressure is P₃ = P [(V-v) / V]³Similarly, if we remove n TIMES volume v, then pressure will be