Question

A big container having ideal gas at pressure $P_0$ and of volume $V_0$ is being evacuated by using vacuum pump of cylinder volume $V$. Find the pressure in the big container after n strokes. (Assume the whole process to be isothermal)

• A. $P_n=P_0{\left(\frac{v_0}{v_0-v}\right)}^n$
  
  
• B. $P_n=P_0{\left(\frac{v_0}{v_0+v}\right)}^n$
  
  
• C. $P_n=P_0{\left(\frac{v_0-v}{v_0+v}\right)}^n$
  
  
• D. $P_n=P_0{\left(\frac{v_0+v}{v_0-v}\right)}^n$
  
  

Answer 1

The correct option is B $P_n=P_0{\left(\frac{v_0}{v_0+v}\right)}^n$



Say pressure before and after stroke to be $P_0,P_1$ respectively.


$P_i{v}_i=P_f{v}_f$

$P_0{v}_0=P_1(v_0+v)$

$P_1=\frac{P_0{v}_0}{v_0+v}$

For the next stroke $P_i=P_1$ and $P_f=P_2$

$P_1{v}_0=P_2(v_0+v)$

$P_2=\frac{P_1{v}_0}{v_0+v}$

Similarly
$P_3=\frac{P_2{v}_0}{v_0+v}$

$P_2=P_0{\left(\frac{v_0}{v_0+v}\right)}^2$

$P_3=P_0{\left(\frac{v_0}{v_0+v}\right)}^3$

$P_n=P_0{\left(\frac{v_0}{v_0+v}\right)}^n$