An air pump has a cylinder 0.260 m long with a movable piston. The pump is used

Question

An air pump has a cylinder 0.260 m long with a movable piston. The pump is used to compress air from the atmosphere (at absolute pressure 1.01 × 105 Pa ) into a very large tank at 3.60 × 105 Pa gauge pressure. (For air, CV = 20.8 J/molK.)

Part A

The piston begins the compression stroke at the open end of the cylinder. How far down the length of the cylinder has the piston moved when air first begins to flow from the cylinder into the tank? Assume that the compression is adiabatic.

Express your answer with the appropriate units.

Answer = 0.172m

Part B

If the air is taken into the pump at 29.0 C, what is the temperature of the compressed air?

Answer = 193 degree C

Part C

How much work does the pump do in putting 25.0 mol of air into the tank? Express your answer with the appropriate units.

Answer = ???

Explanation / Answer

p1 = 1.01 x 10^5 Pa

p2 = 3.6 x 10^5 + 1.01 x 10^5 = 4.61 x 10^5 pa

V1 = h1A

V2 = h2A

y = cp/cv = (cv +R)/cv = 1.40

this is adiabatic process

p1v1^y = p2v2^y

p1(h1A)^y = p2(h2A)^y

h2 = h1(p1/p2)^1/y

h2 = 0.0879 m

T1V1^y-1 = T2V2^y-1

T2 = T1(h1/h2)^y-1

T2 = 300(0.260/0.0879)^1.4-1

T2 = 462.93 K

W = nCv(T1-T2)

W = 25 * 20.8 ( 300 - 462.93) = -84723.65 J

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