Two 2.15 103-kg cars both traveling at 25.0 m/s undergo a head-on collision and

Question

Two 2.15 103-kg cars both traveling at 25.0 m/s undergo a head-on collision and stick together. Find the change in entropy of the surrounding air resulting from the collision if the air temperature is 22°C. Ignore the energy carried away from the collision by sound.

Two 2.15 x 103 kg cars both traveling at 25.0 m/s undergo a head-on collision and stick together. Find the change in entropy of the surrounding air resulting from the collision if the air temperature is 22°C. Ignore the energy carried away from the collision by sound. J/K

Explanation / Answer

This is an example of an inelastic collision, in which momentum, but not kinetic energy, is conserved. After the collision, the two cars are stuck together and motionless. We will assume that none of the initial kinetic energy of the cars is stored as elastic deformation of the destroyed vehicles and that all the initial kinetic energy goes into heating the wrecks (by plastic deformation and friction), that this thermal energy is eventually transferred to the surroundings at 22°C = 295.15K

Initially, the two cars have a combined kinetic energy of 2*(1/2)*(2150 kg)*(25 m/s)^2 = 1343750 J

When this thermal energy is transferred to the surroundings, the entropy change of the universe is:

S = (1343750 J)/(295.15 K) = 4553 J/K

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