Question

A vertical cylindrical tank contains 1.80 mol of an ideal gas under a pressure of 0.300 atm at 20.0°C. The round part of the tank has a radius of 10.0 cm, and the gas is supporting a piston that can move up and down in the cylinder without friction. There is a vacuum above the piston. (a) What is the mass of this piston? (b) How tall is the column of gas that is supporting the piston?

Answer 1

Answer:

Part A $m = 97.37$ Kg

Part B $H = 4.59$ meters

Explanation:

Part A

Pressure is equal to force per unit area

$P = \frac{F}{A}$

Here force is equal to the weight of the piston

Thus

$P = \frac{m*g}{A}$

On rearranging the equation, we get -

$m = \frac{PA}{g}$$m = \frac{P\pi r^2}{g}$

Substituting the given values we get

$m = \frac{0.3*1.013*10^5*0.1^2}{9.8} \\m = 97.37$

Part B

We know that

$V = \pi r^2h$

On substituting the given values we get -

$pV = nRT\\V = \frac{nRT}{p}$

$V = \frac{1.8*8.314*293}{0.3039*10^5} \\V = 0.1442 m^3$

Height

$= \frac{V}{\pi r^2} \\= \frac{0.1442}{\pi 0.1^2} \\= 4.59$