Thermodynamics problem (a little difficult)?

Question

In the sucker of a cylinder there is 28 g Nitrogen in the temperature: t1= 0’ C. The sucker with section S= 100 cm2, through a drum system is connected to an object with weight 500 N. The cylinder is heated and it reaches the temperature: t2= 100’ C. Find the height in which the object goes down. The pressure of the atmosphere is 1 atm. (The weight of the sucker and the friction is not to be considered.)

Answer 1

PV=kT
P1V1/T1 = P2V2/T2
P1 = 1 atm = 101325 N/m^2
V1 = 22.4 l
T1 = 273.15 K
P2 = 1 atm - 500/100 N/cm^2
V2 = ?
T2 = 373.15 K
Convert V1 to m^3
Convert P2 to N/m^2
Solve equality for V2
Divide V2-V1 by S (in m^2) to find height change.