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## Homework Statement

A cylinder of height 1[m] has a weightless piston on it's head. mercury is spilled slowly on the piston and it goes in. at what distance will the mercury start to spill over the cylinder. the process is at constant temperature.

## Homework Equations

$$PV=nRT$$

At constant temperature: P

_{1}V

_{1}=P

_{2}V

_{2}.

The density of mercury: ρ=13.6[gr/cm

^{3}]

Hydrostatic pressure: ##P=h\rho g##

Definition of 1[atm]=101,325[pa=N/m[SUP]3[/SUP]]

3. The Attempt at a Solution

3. The Attempt at a Solution

The pressure of the mercury: ##P=h\cdot 13,600\left[\frac{kg}{m^3}\right]\cdot 9.8\left[\frac{m}{sec^2}\right]=133,280\cdot h##

A is the base area of the cylinder.

$$101,325[pa]\cdot A\cdot 1[m]=133,280\cdot h\cdot (1-h)\cdot A$$

$$\rightarrow h^2-h+0.76=0$$

And it gives a negative discriminant