physics
posted by Jessi .
A cylinder that has a 40.0 cm radius and is 50.0 cm deep is filled with air at 20.0°C and 1.00 atm. A 21.0 kg piston is now lowered into the cylinder, compressing the air trapped inside. Finally, a 79.0 kg man stands on the piston, further compressing the air, which remains at 20°C.
(a) How far down (Ä h) does the piston move when the man steps onto it?
(b) To what temperature should the gas be heated to raise the piston and the man back to h(initial)?
I don't know where to start from here. Do you have to a change in volume type problem? Or could you do it using the ideal gas law?

radius = .4 m so piston area = pi(.16) =.506 m^2
(a) is a change in volume problem all apparently at constant temperature = 293 K
First new volume with the piston:
P1V1/T1 = P2V2/T2
T1=T2 = 293 K
so
V2 = V1 (P1/P2)
P1 = 1 atm = 10^5 Pascals
P2 = 1 atm + (21*9.8)/.506 = 10^5+407
=100,407 Pascals
V2/V1 = 100000/100407 =.996
so
H2 = .996 (50) = 49.8 cm hardly moves
now add the man
V3 = V1(P1/P3)
P3 = 1 atm + (100*9.8)/.506 =10^5+1937
=101,937 Pascals
V3/V1 = 100000/101937 = .981
so
H3 = 50*.981 = 49.05 cm
so
when the piston was added the level went down to 49.8 and then it went down to 49.05 when the man stepped on so it went down about .8 cm due to the man.
For Part V
V2/V1 = 50/49.05 = 1.02
constant pressure so temp goes up
P1V1/T1 = P2 V2/T2
so
V2/V1 = T2/T1
T1 = 293 K
1.02 = T2/293
T2 = 298.7 K = 25.7 C 
thank you so much! it's really clear now with the way you've explained it

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