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]
Generally the volume of air before the bottle is turned upside down is
[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]
