Question

Can someone help me with the problem, thanks. I need help with part b

1. the surface area of the unclothed person is 1.5 m^2 and their skin temperature is 33 C. this ideal person is located in equilibrium with your skin and have the same temperature and emissivity e= 0.95. suppose the room has dimensions of 4m X 9m X 18m.

a) suppose you and your closest 10 friends come into this room and heat it up. suppose your clothes are in equilibrium with your skin and have the same tempertature and emissivity. Further suppose that your net power into the room remains Constanta very bad approximation. How long does it take before the room to get too hot, say 95 F?

b) how does this compare to the rate of 230 W suggested in the book?

Answer 1

Rate at which heat is emitted by 1 person=emissivity*stefan constant*(T^4-T_surrounding^4)*Area

Let surrounding temperature initially =300K

=0.95*5.67*10^-8*(306^4-300^4)*1.6

=53.94W

For Ten persons =53.94*10

=539.4W

Clearly we have made this approximation that surrounding temperature remains constant.However with time surrounding temperature increases and the temperature difference decreases.

Thus the above value is incorrect and is higher than the actual value.

The actual value is 230W as stated.

For a more accurate value we need to have the initial room temperature and consider other factors such as humidity conduction and several other fatcors