Air pump is pumping out a gas from a vessel (vessel's volume is V).(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Air pump physics problem

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