An auditorium of size 40m x 20m x 8m has 600 people init. The temperature of the

Question

An auditorium of size 40m x 20m x 8m has 600 people init. The temperature of the air is 27 degrees C. Ittakes 29 J of thermal energy to raise the temperature of 1 mol ofair by 1 K and the molar mass of air is 29 g/mol. Take thedensity of air to be constant at 1.25 kg/m3. a) How many moles of air are there in the auditorium? b)Assuming that each person gives off thermal energy at a rateof 80 W, calculate how fast the temperature in the auditorium isrising. Assume that the auditorium is closed so that coolerair does not enter. An auditorium of size 40m x 20m x 8m has 600 people init. The temperature of the air is 27 degrees C. Ittakes 29 J of thermal energy to raise the temperature of 1 mol ofair by 1 K and the molar mass of air is 29 g/mol. Take thedensity of air to be constant at 1.25 kg/m3. a) How many moles of air are there in the auditorium? b)Assuming that each person gives off thermal energy at a rateof 80 W, calculate how fast the temperature in the auditorium isrising. Assume that the auditorium is closed so that coolerair does not enter.

Explanation / Answer

   n = m / molarmass
Where m = density x volume
   =( 1250 g / m3 )x ( 40x20x8)m3  
   =8x106 g
  number of moles = 8x106 g / ( 29g/mol)
      = 2.758x105moles
Power at which a person releases heat P = 80W
   The rate at which the temperature is risingis
   = (29 J / m.K ) /(80J/s)
   = 0.3625s / m.K      

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