# A vertical cylinder of cross-sectional area 0.050m^2 is fitted with a tight-fitting, frictionless pistionof mass 5.0 kg. If there are 3.0 mol of ideal gas in the cylinderat 500 K, determine the height "h" at which the postion will be inequilibrium.

A vertical cylinder of cross-sectional area $$\displaystyle{0.050}{m}^{{2}}$$ is fitted with a tight-fitting, frictionless pistionof mass 5.0 kg. If there are 3.0 mol of ideal gas in the cylinderat 500 K, determine the height "h" at which the postion will be inequilibrium.

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Asma Vang

A vertical cylinder ofcross-sectional area 0.050 $$\displaystyle{m}^{{2}}$$ is fitted with atight-fitting, frictionless pistion of mass 5.0 kg. If there are 3.0 mol of ideal gas in the cylinder at 500 K, determine the height"h" at which the postion will be in equilibrium.
the height "h" at which thepostion will be in equilibrium can be found by using $$\displaystyle{h}={\frac{{{V}}}{{{A}}}}$$
according to ideal gaslaw $$V=\frac{nRT}{P} n = 3.0 mol , T= 500 K , R = 8.31 J/ mol .K$$
Where $$\displaystyle{P}_{{{a}{t}{m}}}+{P}_{{{g}{a}{u}\ge}}$$
$$\displaystyle{P}_{{{a}{t}{m}}}={1.013}\cdot{10}^{{5}}$$ Pa
$$\displaystyle{P}_{{{g}{a}{u}\ge}}={\frac{{{F}}}{{{A}}}}$$
$$\displaystyle={\frac{{{m}{g}}}{{{A}}}}$$
where m is mass =5.0kg, $$\displaystyle{g}={9.8}\frac{{m}}{{s}^{{2}}}$$
A is area $$\displaystyle={0.050}{m}^{{2}}$$
plug the values in corresponding equations and calculatea for the answer