Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

EXAMPLE 4–13 Temperature Rise due to Slapping

If you ever slapped someone or got slapped yourself, you probably remember

the burning sensation. Imagine you had the unfortunate occasion of being

slapped by an angry person, which caused the temperature of the affected

area of your face to rise by 1.8°C (ouch!). Assuming the slapping hand has a

mass of 1.2 kg and about 0.150 kg of the tissue on the face and the hand

is affected by the incident, estimate the velocity of the hand just before

impact. Take the specific heat of the tissue to be 3.8 kJ/kg · °C.

Solution The face of a person is slapped. For the specified temperature

rise of the affected part, the impact velocity of the hand is to be determined.

Assumptions 1 The hand is brought to a complete stop after the impact.

2 The face takes the blow without significant movement. 3 No heat is trans-

ferred from the affected area to the surroundings, and thus the process is

adiabatic. 4 No work is done on or by the system. 5 The potential energy

change is zero, PE 0 and EUKE.

Analysis We analyze this incident in a professional manner without involving

any emotions. First, we identify the system, draw a sketch of it, and state

our observations about the specifics of the problem. We take the hand and

the affected portion of the face as the system(Fig. 4–36). This is a closed

system since it involves a fixed amount of mass (no mass transfer). We

observe that the kinetic energy of the hand decreases during the process, as

evidenced by a decrease in velocity from initial value to zero, while the inter-

nal energy of the affected area increases, as evidenced by an increase in the

temperature. There seems to be no significant energy transfer between the sys-

tem and its surroundings during this process.

Under the stated assumptions and observations, the energy balance on the

system can be expressed as

Net energy transfer Change in internal, kinetic,

by heat, work, and mass potential, etc., energies

That is, the decrease in the kinetic energy of the hand must be equal to the

increase in the internal energy of the affected area. Solving for the velocity

and substituting the given quantities, the impact velocity of the hand is

determined to be

Discussion Reconstruction of events such as this by making appropriate

assumptions are commonly used in forensic engineering.

41.4 m>s 1 or 149 km>h 2



B

21 0.15 kg 21 3.8 kJ>kg #°C 21 1.8°C 2

1.2 kg

a

1000 m^2 >s^2

1 kJ>kg

b

Vhand

B

21 mc¢T (^2) affected tissue
mhand
0  1 mc¢T (^2) affected tissue 3 m 10
V^2 2> (^24) hand
0 ¢Uaffected tissue¢KEhand
Ein
Eout¬
¬
¢Esystem
192 | Thermodynamics
FIGURE 4 –36
Schematic for Example 4 –13.
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