- #1
Yegor
- 147
- 1
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.
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.