A train crashes against a shock-absorber pneumatic consisting of two identical c

Question

A train crashes against a shock-absorber pneumatic consisting of two identical cylinders 75 cm long and with 25cm of diameter filled with air at a pressure of p=1 Kp/cm2 and T=22 C. After the crash, the pistons of the cylinder recoil 60 cm. Compute the final pressure and temperature of the air inside the cylinder and the total work done on each cylinder. The air density is 0.001293 g/cm

. The specic heat of air is Cp= 0.24 and Cv= 0:16 cal/g C. Explain how energy is conserved in this
problem (you can make estimates for the mass of the train if you wish).

Explanation / Answer

=Cp/Cv=1.5

P1V1=P2V2

=>P2=1096.45 Pa

T1V1-1= T2V2-1

=>T2=659.64 K

W=(P2V2-P1V1)/(1-) = -8.925 J

The kinetic energy of the train is converted into work done on the air inside the cylinders.

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