A cylindrical vessel of 28 cm diameter contains 20 g of nitrogen compressed by a piston supporting a weight of 75 kg. The temperature of the gas is `17^(@)C`. What work will the gas do if it is heated to a temperature of `250^(@)C` ? What amount of heat should be supplied ? To what distance will the weight be raised? The process should be assumed to be isobaric, the heating of the vessel as well as the external pressure is negligible.

Explanation

`Delta W` (work done)
`= int p Delta V = p (m)/(M) (R Delta T)/(p) = (m)/(M) R Delta T`
`:. Delta w = (20)/(28) 8.3 (250 - 17) = 1381 J`
`Delta U = (m)/(M) C_(v) Delta T = (m)/(M) (R )/(gamma - 1) Delta T`
`= (20)/(28) xx (8.3)/((7)/(5) - 1) xx (250 - 17) = 3453 J`
`:. Delta Q = Delta W + Delta U = 1381 + 3453 = 4834 J`
`DeltaW` is also equal ot `mgh` (see the above problem).
`:. 1381 = 75 xx 9.8 xx h`
or `h = 1.88 m`