$1-106$ The pressure of a gas contained in a vertical piston$-$cylinder device is measured to be $180$kPa. The mass of the piston is to be determined.

Assumptions There is no friction between the piston and the cylinder.

Analysis Drawing the free body diagram of the piston and balancing the vertical forces yield

$W=PA-P_{\text{a}\text{t}\text{m}}A$

$mg=(P-P_{\text{a}\text{t}\text{m}})A$

$(m)(9\mathrm{.}81\frac{m}{s^2})=(180-100$kPa$)(25{10}^{-4}{m}^2)(\frac{1000\frac{kg}{m}*s^2}{1\text{k}\text{P}\text{a}})$

It yields $,m=20\mathrm{.}4kg$