17-4) A disposable medical syringe with the needle removed and the tip plugged u

Question

17-4) A disposable medical syringe with the needle removed and the tip plugged up makes a good piston. Consider a syringe that has a diameter of 1.8 cm.
(a) If you compress the air trapped in the piston by pushing on the syringe's plunger with an average force of 2.0 N for a distance of 0.55 cm., how much mechanical work do you do on the gas?
(b) What is the pressure exerted on the syringe?
(c) How much does the volume of the trapped air change as a result of the distance the plunger moves?
(d) Use the pressure and volume change to calculate the work.
(e) Are the answers to part (a) and (d) the same? Did you expect them to be the same? Why or why not?

Explanation / Answer

a) W = Fd = 2.0x0.55x10-2 = 1.1x10-2 J

b) cross section area A = d2/4 = *(1.8x10-2)2 /4 = 2.54469 x 10-4 m2

P = F/A = 2.0 /(2.54469x10-4) = 7.86 x103 Pa

c) volume decreased by V = Ad = 2.54469 x 10-4 x 0.55x10-2 = 1.40x10-6 m3

d) W = PV = 7.86x103 x 1.40x10-6 = 1.1x10-2 J

e) same. I expect them to be same because of conservation of energy.

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