Calculating the Temperature Needed to Move a Piston in a Sealed Cylinder

In summary, the person is trying to figure out how much more pressure they need to lift the piston in order to heat up the air inside the can. They found that using the equation of state, the pressure needed is greater than the weight force of the piston. They believe that the standard air temp at sea level is approx 288K, so they add 10K to that to get 299K.
  • #1
npau8648
2
0
Hey all, I'm trying to do some math related to air pressure and temperature and i keep getting unreasonable answers.

What i have is a cylinder (topless, diameter 3.5cm and height 10cm) with a piston placed inside it (diameter approx 3.5cm height 4 cm). Piston weights around .5kg. Piston is currently hanging around 3cm from the bottom of the cylinder and cylinder is air sealed by a balloon. - (Trying to to an experiment kinda like a sterling engine)

Wat I am trying to do is heat up the bottom of the can, in turn heating up the air in the bottom of the can. This increase in air temp should increase the pressure (i think). F = pA, where A is the surface area of the bottom of the piston.

So wat I am trying to do is find wat temperature the air will need to be heated to before the piston will be moved up.

So I've gone:

pA > mg (The force exerted by the pressure must be greater than the weight force of the piston)

so,

p > (1.5*9.81)/(PI*.035^2)
p > 3823,62 Pa

Which already sounds a lil wrong to me.

So i keep going anyway.

Using the equation of state ( i think that's wat its called ):

P = rRT (r = rho)
R = 287

Therfore, rRT > 3823,62

T > 3823.62/(rR)

For r i used the standard density of air at sea level - 1.229 kg/m^3

so T > 3823.62/(1.229 * 287)
T > 10 K

Which really just can't be right lol I have no idea what I am doing wrong. I don't do physics or any science infact, I've tried gathering this information from various sites today, so my mistake or misunderstanding is probably obvious.

Any help would be greatly appreciated :)
 
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  • #2
You just figured on how much more pressure you need to lift the piston. That's extra pressure above atmospheric pressure. So what does that tell you about that 10K...?
 
  • #3
So standard air temp at sea level is approx 288K, so add 10K. So 299K is needed.

Dont want to be a pain, but i don't exactly understand how i only calculated "extra pressure above atmospheric pressure". Would i be right in saying atmospheric pressure is acting on both ends of my piston (101300 Pa) and hence i should have:

pA (Total force exerted by pressure in bottom of can) > mg + 101300(A)

Just making sure i have the right idea.

Thanks for your quick reply btw!
 

What causes changes in air pressure?

Air pressure is caused by the weight of the air above a certain point. It is affected by temperature, altitude, and the movement of air particles.

How do air pressure and temperature relate to each other?

As temperature increases, air molecules gain energy and move faster, causing them to spread out and create a lower pressure. As temperature decreases, air molecules slow down and become more compact, creating a higher pressure. This relationship is known as the ideal gas law.

Why do airplanes need to consider air pressure and temperature?

Air pressure and temperature affect the density of the air, which in turn affects the lift and thrust of an airplane. Pilots need to consider these factors to ensure safe and efficient flight.

How does air pressure and temperature impact weather?

Changes in air pressure and temperature can lead to changes in weather patterns. High pressure areas generally bring clear, dry weather, while low pressure areas are associated with rain and storms. Temperature also plays a role in the formation of clouds and precipitation.

How is air pressure and temperature measured?

Air pressure is measured using a device called a barometer, which can be either aneroid (measuring changes in air pressure) or mercury (measuring absolute air pressure). Temperature is typically measured with a thermometer, which can be either a liquid-filled or electronic device.

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