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

Question

A vertical cylinder, closed at the bottom and fitted on top with a piston, contains air initially at 27C with a volume of 320cm3. The piston is held in place externally by an elastic spring with the atmposhere at 1.00bar, and the weight of the piston which is 90N. The initial spring force is 448N, and spring constant is 160N/cm, and the piston area is 64cm2. During a process heat is added until the final air pressure is 2.75bars. Determine (a) the work done on the piston (J), (b) the net work done on the piston by the gas (J), (c) the temperature change of the air (C), and (d) the heat transfer (J).

Explanation / Answer

a)

0

b)

initial:

xi = Fi/k = 448/16000 = 0.028 m

final:

P = 2.7 bar - 1 bar = 1.7e5 Pa

Ff = P A - mg = 1.7e5 * 64e-4 - 90 = 998 N

xf = Ff/k = 998/16000 = 0.062375 m

the work done by the spring = Ws

Ws = 0.5 k (xf^2 - xi^2) = 0.5* 16000*(0.062375*0.062375-0.028*0.028) = 24.853 J

the work done by the atmosphere = Wa

Wa = F d = P A (xf - xi) = 1e5*64e-4*(0.062375-0.028) = 22 J

the work done by the gravity = Ww

Ww = F d = m g (xf - xi) = 90*(0.062375-0.028) = 3.09375 J

the work done by gas = Wg

Wg = Ws + Wa + Ww = 24.853 + 22 + 3.09375 = 49.94675 = 49.9 J

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