Thermodynamics

⎫ ⎪⎬⎪⎭⎫⎪⎬⎪⎭192 | ThermodynamicsEXAMPLE 4–13Temperature Rise due to SlappingIf you ever slapped someone or got slapped yourself, you probably rememberthe burning sensation. Imagine you had the unfortunate occasion of beingslapped by an angry person, which caused the temperature of the affectedarea of your face to rise by 1.8°C (ouch!). Assuming the slapping hand has amass of 1.2 kg and about 0.150 kg of the tissue on the face and the handis affected by the incident, estimate the velocity of the hand just beforeimpact. Take the specific heat of the tissue to be 3.8 kJ/kg · °C.FIGURE 4–36Schematic for Example 4–13.Solution The face of a person is slapped. For the specified temperaturerise 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 transferredfrom the affected area to the surroundings, and thus the process isadiabatic. 4 No work is done on or by the system. 5 The potential energychange is zero, PE 0 and E U KE.Analysis We analyze this incident in a professional manner without involvingany emotions. First, we identify the system, draw a sketch of it, and stateour observations about the specifics of the problem. We take the hand andthe affected portion of the face as the system (Fig. 4–36). This is a closedsystem since it involves a fixed amount of mass (no mass transfer). Weobserve that the kinetic energy of the hand decreases during the process, asevidenced by a decrease in velocity from initial value to zero, while the internalenergy of the affected area increases, as evidenced by an increase in thetemperature. There seems to be no significant energy transfer between the systemand its surroundings during this process.Under the stated assumptions and observations, the energy balance on thesystem can be expressed asE in E out Net energy transferby heat, work, and mass¢E systemChange in internal, kinetic,potential, etc., energiesThat is, the decrease in the kinetic energy of the hand must be equal to theincrease in the internal energy of the affected area. Solving for the velocityand substituting the given quantities, the impact velocity of the hand isdetermined to beV hand B2 1mc¢T2 affected tissuem hand0 ¢U affected tissue ¢KE hand0 1mc¢T2 affected tissue 3m 10 V 2 2>24 hand B2 10.15 kg213.8 kJ>kg # °C211.8°C21.2 kg 41.4 m>s 1or 149 km>h2a 1000 m2 >s 21 kJ>kg bDiscussion Reconstruction of events such as this by making appropriateassumptions are commonly used in forensic engineering.