What is the piston height if the temperature is 30C?...physics help please?

Question

The 50 kg circular lead piston (10 cm wide cylinder) floats on 0.360 mol of compressed air.

What is the piston height if the temperature is 30C?

How far does the piston move if the temperature is increased by 100 C?

I know this much so far:

Pressure=Force/ area = (50)(9.8)/pi(R)^2 = 490/piR^2

using orginal formula PV=nRT

Vcylinder=pi * R^2 * H = (3.14)(5^2)(H)

can someone please help with the rest?

Answer 1

Let's use SI units:

pressure = 50 * 9.8 / pi / 0.05^2 = 62400 Pa

Important to realize that this is GAGE pressure, not absolute, (there is one atm pressure also pushing on the piston) so add 101300 Pa

P = 163700 Pa (absolute)

n = 0.360

R = 8.314 m^3 Pa /K mole

T = 273 + 30 = 303 K (absolute)

solving for V:

V = 0.0554 m^3

volume of cylinder = pi * r^2 * h

h = 0.705 m

increasing the temperature by 100 C:

T goes from 303K to 403K, or 1.33 x

So volume also increases by 1.33 x

And h also increases by 1.33 x

(P, n and area are constant)

change in h = 0.33 (0.705) = 0.23 meters