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THERMODYNAMICS - CASE STUDY SOLUTION

 

The velocity of a 1.2 kg hand needs to cause the face temperature to rise 1.8 oC when slapped. The kinetic energy of the hand decreases during the process, due to a decrease in velocity from the initial value to zero. At the same time, the internal energy of the affected area increase, due to an increase in the temperature.

Assumptions:

  • The hand is brought to a complete stop after the impact and the face does not move.
  • No heat is transferred from the affected area to the surroundings. No work is done to or by the system.
  • The potential energy change is zero.
   


System

The energy balance equation:  

      Ein - Eout = Δ Esystem
              = (ΔU + ΔKE + ΔPE)affected tissue +
                 (ΔU + ΔKE + ΔPE)hand

With all these assumptions, the equations can be simplified as:

Plug in the numbers, the solution for velocity v is:

      0 = (mcDT)affected tissue + [m(0 - v2)/2]hand

      

This is a very fast hand.