Question

A gas is confined in a 0.3m diameter cylinder by a piston, on which rests a weight. The mass of the piston is 85 kg. The local acceleration of gravity is 9.807 m/s, and atmospheric pressure is 101.33 kPa. If the absolute pressure of the gas is 1.4 bar, calculate the mass in kilograms of the weight.

Answer 1

Explanation:

Force applied on the gas will be as follows.

                   $F_{gas} = F_{atm} + (m + M) g$

As,   F = pressure × area. Hence, calculate the forces as follows.

                  $F_{gas}$ = pressure × area

                         = $1.4 \times 10^{5} Pa \times \pi \times (\frac{0.3}{2})^{2}$

                          = $1.979 \times 10^{4}$ N

                  $F_{atm}$ = pressure × area

                            = $1.0133 \times 10^{5} \times \pi \times (\frac{0.3}{2})^{2}$

                            = $1.432 \times 10^{4}$ N

      $F_{gas}$ - $F_{atm}$ = $5.47 \times 10^{3}$ N

Substituting the calculated values into the above formula as follows.

                $F_{gas} = F_{atm} + (m + M) g$

              $F_{gas} - F_{atm}$ = (m + M) g

              $5.47 \times 10^{3}$ N = $(m + 85) \times 9.8$    

              $5.47 \times 10^{3}$ N = $9.8m + 833$

                               m = 472.76 kg

Thus, we can conclude that the mass is 472.76 kg.