The pressure gauge shown in figure has a spring for which `k=60N//m` and the area of the piston is `0.50cm^(2)`. Its right end is connected to a closed container of gas at a gauge pressure of `30kPa`. How far will the spring be compressed if the region containing the spring is (a) in vacuum and (b) open to the atmosphere? Atmospheric pressure is `101kPa`.

Explanation

(i) 10.9 cm (ii) 2.5 cm
(i) Pressure to the right of piston, P ` = (30 + 101 ) k Pa = 131 kPa `
Compressive force, F ` = PA = (131 xx 10 ^(3) Pa ) (0.50 xx 10 ^(-4) m ^ 2 ) = 6.55 N `
As ` F = kx, x = (F)/(k) = (6.55 N ) /(60 N//m) = 0.109 m = 10.9 cm `
(ii) The force is now due to the gauge pressure (30 kPa) acting on the piston area and is given by
` F' = (30 xx 10 ^(3) Pa ) ( 0.50 xx 10 ^( - 4 ) m ^ 2 ) = 1.5 N , x = (F' )/(k) = (1.5 N ) /( 60 N//m) = 0.025 m = 2.5 cm `