Question

The pressure gauge shown in figure has a spring for which $k=60N/m$ and the area of the piston is $0.50c{m}^2$ . Its right end is connected to a closed container of gas at a gauge pressure of $30kPa$. How far will the spring be compressed in the region containing the spring is (a) in vacuum and (b) open to the atmosphere? Atmospheric pressure is $1001kPa$,

Answer 1

(a) Force from left hand side=force from right hand side
$\therefore$ $kx=\Delta pA$
or $x=\frac{\left(\Delta p\right)A}{k}$
$=\frac{(30+101)\times {10}^3\times 0.5\times {10}^{-4}}{60}$
$=0.109$ m or $10.9$ cm
(b) $x=\frac{\left(\Delta p\right)A}{k}=\frac{30\times {10}^3\times 0.5\times {10}^{-4}}{60}$
$=0.025$ m$=2.5$ cm