Air pump is pumping out a gas from a vessel (vessel's volume is V). After each cycle i it pumps out dV. Gas is ideal. T=Const. After how much cycles pressure P will decrease k times? Here is my work. PV = nRT Initially n=n(0) After each cycle n decreases (1-dV/V) times. So, after x cycles n(x)=n(0)(1-dV/V)^x k=p(0)/p(x)=n(0)/n(x) n(x)/n(0)=(1-dV/V)^x So x =ln(1/k)/ln(1-dV/V) But the answer is x=ln(k)/ln(1+dV/V) As I understand, they assume that after each cycle n decreases 1/(1+dV/V) times. In this way i really receive x=ln(k)/ln(1+dV/V) I don't understand it. Help me please.