A vertical cylinder closed at the bottom and fitted on top with a piston, contai

Question

A vertical cylinder closed at the bottom and fitted on top with a piston, contains air initially at 27C with a volume of 320cm^3. The piston is held in place externally by an elastic spring, the atmosphere is at 1 bar and the weight of the piston is 96N. The initial spring froce is 448N, the spring constant is 160N/cm, and the piston area is 64cm^2. During a process heat is added until the final air pressure is 2 bars.

Find:

a.) The work done on the piston, in joules.

b.) The net work on the piston by the gas in joules.

c.) Temperature change of the air in Celcius.

d.) The heat transfer in joules.

Explanation / Answer

pressure due to spring and piston = (448+96)/64 = 8.5N/cm^2

atm pressure = 1bar = 10N/cm^2

Total pressure = 18.5N/cm^2

When the pressure is increased to 2bar = 20N/cm^2

increase in pressure = 1.5N/cm^2

Extra force on spring = 1.5*64 = 96N

a) kx1 = 448

160x1 = 448,

x1 = 2.8cm

160x2 = 448+96

x2 = 3.4cm

a) workdone on piston = 0.5kx2^2 - 0.5kx1^2 = 0.5*160*(3.4^2 - 2.8^2) = 297.6Ncm = 2.97Nm = 2.97J

b) same = 2.97J

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