Thermodynamics

[25thhour]

Hey guys, I am having trouble with some stupid thermodynamics questions...

I don't know what formulas to use and its kinda frustrating. I can't derive them.

1. The figure shows a 50-kg frictionless cylindrical piston that floats on 0.68 mol of compressed air at 30°C. How far does the piston move if the temperature is increased to 300°C? The piston is 10cm long. I have done this one countless times and I keep getting 311cm as a change in height.

mgh = nRT
is the formula I use and I do it twice and subtract what I get at 573K from what I get at 303K. This is really frustrating me.

2.
The figure (not to scale) shows a pV diagram for 1.8 g of helium gas (He) that undergoes the process 1 → 2 → 3. Find the value of V3. The ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K, and the atomic weight of helium is 4.0 g/mol.

At point 1
P1 = 2 ATM
T1 = 37 C
V1 = ?

At Point 2
P2 = ?
T2 = 657 C
V2 = V1 = ?

At Point 3
P3 = P1 = 2ATM
T3 = ?
V3 = ?

I am totally lost on this one... I have tried to make equations to find one of the missing variables for P3 but failed I basically just keep ending up with this equation.

(2atm)V3 = (.036945)(T3) Have tried solving many times but end up with

xV3 = yV3


3. A cubical box, 5.00 cm on each side, is immersed in a fluid. The pressure on the bottom surface is 539 Pa higher than the pressure on the top surface. What is the density of the fluid?

Ya so I have gotten to the answer 11000N/m^3
But thats not density...

Will give credits to whomever helps me