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

Step-by-step 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 * 10^(5) Pa * \pi * ((0.3)/(2))^(2)`

=
`1.979 * 10^(4)` N

`F_(atm)` = pressure × area

=
`1.0133 * 10^(5) * \pi * ((0.3)/(2))^(2)`

=
`1.432 * 10^(4)` N

`F_(gas)` -
`F_(atm)` =
`5.47 * 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 * 10^(3)` N =
`(m + 85) * 9.8`

`5.47 * 10^(3)` N =
`9.8m + 833`

m = 472.76 kg

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