Explanation:
Force applied on the gas will be as follows.
[tex]F_{gas} = F_{atm} + (m + M) g[/tex]
As, F = pressure × area. Hence, calculate the forces as follows.
[tex]F_{gas}[/tex] = pressure × area
= [tex]1.4 \times 10^{5} Pa \times \pi \times (\frac{0.3}{2})^{2}[/tex]
= [tex]1.979 \times 10^{4}[/tex] N
[tex]F_{atm}[/tex] = pressure × area
= [tex]1.0133 \times 10^{5} \times \pi \times (\frac{0.3}{2})^{2}[/tex]
= [tex]1.432 \times 10^{4}[/tex] N
[tex]F_{gas}[/tex] - [tex]F_{atm}[/tex] = [tex]5.47 \times 10^{3}[/tex] N
Substituting the calculated values into the above formula as follows.
[tex]F_{gas} = F_{atm} + (m + M) g[/tex]
[tex]F_{gas} - F_{atm}[/tex] = (m + M) g
[tex]5.47 \times 10^{3}[/tex] N = [tex](m + 85) \times 9.8[/tex]
[tex]5.47 \times 10^{3}[/tex] N = [tex]9.8m + 833[/tex]
m = 472.76 kg
Thus, we can conclude that the mass is 472.76 kg.
