Answer:
The value is   [tex] P_G  =  2.925 *10^{5} \  Pa[/tex]
Explanation:
From the question we are told that
  The  volume of the bottle is  [tex]v  =  2 \  L  =  2 *  10^{-3} \  m^3[/tex]
  The gauge pressure of the air is [tex]P_g  =  340 \  kPa  =  340 *10 ^{3}  \  Pa[/tex]
 Â
Generally the volume of air before the bottle is turned upside down is Â
   [tex]V_a  =  \frac{3}{4}  * V[/tex]
    [tex]V_a  =  \frac{3}{4}  *  2 *10^{-3}[/tex]
    [tex]V_a  =  0.0015 \  m^3 }[/tex]
Generally the volume air when the bottle is turned upside-down is
   [tex]V_u  =  \frac{5}{6}  *  2 *10^{-3}[/tex]
    [tex]V_u  =  0.00167 \  m^3 [/tex]
From the the mathematical relation of adiabatic process we have that
   [tex]P_g *  V_a^r  =  P_G *  V_u^r[/tex]
Here r is a constant with  a value  r =  1.4
So
   [tex] 340 *10 ^{3}  *  0.0015^{1.4}  =  P_G *  0.00167^{1.4}[/tex]
    [tex] P_G  =  2.925 *10^{5} \  Pa[/tex]
