A 200ton automobile is travelling at 55 mph and brakes to a

A 2.00-ton automobile is travelling at 55 mph and brakes to a complete stop to park. It does not move until the next day. a. Assume the system boundary is the car only. The heat from the brakes gets absorbed by the air around the car. Which terms in the Universal Accounting Equation are non-zero for this system? b. Now, assume the system boundary is the car and the surrounding air that absorbs the heat of the brakes. Which terms in the Universal Accounting Equation are non-zero for this system? c. How much heat (in Btu) was released as the brakes cooled?

Solution

a)
Universal Accounting Equation:
Final Amount - Initial Amount = Amount Entering - Amount Leaving + Amount Generated - Amount Consumed

Using this eqn for Energy,
Final Energy - Initial Energy = Energy Entering - Energy Leaving + Energy Generated - Energy Consumed

In this eqn, non-zero terms will be, Initial Energy = 1/2*mv^2 and Energy leaving = Heat dissipation from brakes to outside air

b)
For car + surroundings, all the terms on right hand side will be zero. Hence, only Final Energy and Initial Energy will be non-zero.

c)
Mass m = 2 ton = 2000 kg
Velocity V = 55 mph = 24.6 m/s
From part a, we have
0 - 1/2*mv^2 = 0 - Energy leaving + 0 - 0
Energy leaving = 1/2*mv^2
= 1/2*2000*24.6^2
= 604530.4 J
= 572.98 Btu