# Air is compressed in a cylinder

• Karol
In summary, a cylinder with a weightless piston on its head has mercury spilled slowly onto it, causing the piston to go down. The question asks at what distance will the mercury start to spill over the cylinder, with the process happening at constant temperature. Using the equations PV=nRT and P1V1=P2V2, as well as the density of mercury and hydrostatic pressure, it is determined that the absolute pressure at the end is the pressure of the mercury plus 1[atm].

## 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: P1V1=P2V2.
The density of mercury: ρ=13.6[gr/cm3]
Hydrostatic pressure: ##P=h\rho g##
Definition of 1[atm]=101,325[pa=N/m[SUP]3[/SUP]]

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

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

Hello. What was the reasoning that led you to this equation?

You're dealing with mercury and air here. One is a liquid, and the other a gas. Can you really use the equation ##p_1V_1 = p_2V_2##?

The mercury doesn't mix with the air, it doesn't enter inside the cylinder. the piston goes down and a cup, a vessel is formed on the top of the cylinder with the piston as the bottom of the cup.
$$101,325[pa]\cdot A\cdot 1[m]=(133,280\cdot h)((1-h)\cdot A)$$
##(133,280\cdot h)## is the new pressure, the pressure of the mercury, P2, and ##((1[m]-h)\cdot A)## is the new volume, V2.
I forgot to state at the beginning that the absolute pressure in the cylinder at the beginning was 1[atm]

I think i solved. the absolute pressure at the end is the pressure of the mercury+1[atm]

Karol said:
I think i solved. the absolute pressure at the end is the pressure of the mercury+1[atm]
OK.

## 1. What is the purpose of compressing air in a cylinder?

Compressing air in a cylinder allows for the storage of a larger volume of air in a smaller space. This can be useful for various applications such as powering tools and machinery, filling tires, and providing compressed air for industrial processes.

## 2. How is air compressed in a cylinder?

Air is compressed in a cylinder using a compressor, which uses mechanical force to decrease the volume of the air and increase its pressure. This can be achieved through various methods such as a piston, rotary screw, or centrifugal compressor.

## 3. What happens to air when it is compressed in a cylinder?

When air is compressed in a cylinder, the molecules are forced closer together, resulting in an increase in pressure and temperature. This increase in pressure and temperature can cause the air to become denser and more powerful, making it useful for various tasks.

## 4. Is it safe to compress air in a cylinder?

While compressing air in a cylinder can be dangerous if not done properly, it is generally considered safe as long as proper safety precautions are taken. This includes using the appropriate equipment, following manufacturer guidelines, and ensuring the cylinder is in good condition.

## 5. What are the benefits of using compressed air in a cylinder?

Using compressed air in a cylinder has several benefits, including its versatility, portability, and cost-effectiveness. Compressed air can also be a clean and efficient source of power, making it a popular choice in various industries and applications.