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

[npau8648]

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 :)

 

[russ_watters]

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...?

 

[npau8648]

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!