Compressibility and heights

In summary, the 20kg man stands on a piston which is lowered into a cylinder filled with air at 20C and 1atm. The pressure remains at 20C but the temperature increases gradually to 25C. When the man steps off the piston, the pressure and temperature return to 20C.
  • #1
thenewbosco
187
0
Here is my problem:

A cylinder with 0.4m radius and 0.5m depth is filled with air at 20C and 1atm.
A 20.0 kg piston is lowered into the cylinder, compressing the air inside. Finally a 75 kg man stands on the piston further compressing the air which remains at 20C.

how far down does the piston move when the man steps on it and to what temp. must the gas be heated to return the man back to the height when the 20kg piston was placed on.

So far i have calculated the number of moles of gas in the container, which will be constant throughout. and i can calculate the force applied when the man and piston are compressing it as mgh. i suppose the h will give me the distance it compresses but i have nothing to equate mgh to...
can someone help me out here
 
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  • #2
...anyone?
 
  • #3
no one can help me with this?
 
  • #4
PV= NRT.

I'm not sure why you would calculate N, the number of moles. Since it remains constant, it will cancel out anyway. You know P, V, and T initially. You add 95kg mass so you can calculate the additional force (weight) and divide by the cross section area of the cylinder to find the additional pressure. I am assuming any heat generated conducts away so the temperature remains the same.

Calling the initial P and V P1 and V1 and the later P and V P2 and V2, you have
[tex]\frac{P_1V_1}{P_2V_2}= \frac{NRT}{NRT}= 1[/tex]
That is, V2= P1V1/P2.

Once you know the volume, of course, you divide by the cross section area of the cylinder to find the height, subtract that from the original height to find how far the piston moves.

For the second part, once again PV= NRT. Now you are maintaining the same pressure while changing the temperature. Writing T1 and T2 for the temperatures before and after (you know that T1= 20 C), we have
[tex]\frac{PV_1}{PV_2}= \frac{NRT_1}{NRT_2}[/tex]
so that T2= T1(V2/V1).
 

1. What is compressibility?

Compressibility refers to the ability of an object or substance to decrease in volume when pressure is applied to it. This is a fundamental property of matter and is influenced by factors such as the material's density and elasticity.

2. How does compressibility affect heights?

As pressure increases with increasing altitude, the air becomes more compressed and thus more dense. This means that the air molecules are closer together and take up less space, leading to a decrease in air pressure and ultimately affecting the height at which objects can travel or be supported.

3. What is the relationship between compressibility and altitude?

The relationship between compressibility and altitude is inverse, meaning that as altitude increases, the compressibility of air decreases. This is because at higher altitudes, the air is less compressed and therefore less dense.

4. How does compressibility impact aircraft design?

Compressibility is a crucial factor in aircraft design as it affects the aerodynamics and performance of the aircraft. This is especially important for high-speed aircraft such as supersonic jets, where compressibility effects must be carefully considered to prevent issues such as shock waves and drag.

5. Can compressibility be measured?

Yes, compressibility can be measured using various techniques such as pressure-volume relationships, adiabatic compressibility, and sound speed measurements. These measurements can provide valuable information about the compressibility and density of a material, which can be used in various scientific and engineering applications.

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