I realize this is asking a little much. However, I have absolutely no idea how t
ID: 1786717 • Letter: I
Question
I realize this is asking a little much. However, I have absolutely no idea how to approach these problems and need some assistance. Much appreciated!
A lamp filament radiates 100 W of power when the temperature of the surroundings is 20°C and it radiates 99.1 W of power when the temperature of the surroundings is 29°C. If the temperature of the filament is the same in each case, what is that temperature on the Celsius scale?
_________________°C
A steel cylinder of radius 3.0 cm and length 6.0 cm is placed in end-to-end thermal contact with a copper cylinder of the same dimensions. If the free ends of the two cylinders are maintained at constant temperatures of 92°C (steel) and 13°C (copper), how much heat will flow through the cylinders in 13 min?
_________________J
A large StyrofoamTM cooler has a surface area of 2.3 m2 and a thickness of 3.0 cm. If 6.8 kg of ice at 0°C is stored inside and the outside temperature is a constant 33°C, how long does it take for all the ice to melt? (Consider conduction only.)
_________________h
Assume that your skin has an emissivity of 0.70, a normal temperature of 34°C and a total exposed area of 0.25 m2. How much heat energy per second do you lose due to radiation per second if the outside temperature is 21°C?
_____________________________ J/s
At what average rate would heat have to be removed from 1.5 L of each of the following to reduce the liquid's temperature from 22°C to its freezing point in 3.1 min?
(a) water
__________W
(b) mercury
_________W
Explanation / Answer
Assuming emissivity E = 1, power P = A(Tfil^4-Ta^4)
(Ta is ambient temp., A is area, is Stefan constant for blackbody radiation = 5.6704E-8 w/m^2K^4. See the ref.)
Thus P is proportional to Tfil^4-Ta^4
Ta1 = 293.15 K, Ta2 = 302.15 K.
P2/P1 = 0.991 = (Tfil^4-Ta2^4)/(Tfil^4-Ta1^4)
0.991Tfil^4-0.991Ta1^4 = Tfil^4-Ta2^4
0.009Tfil^4 = Ta2^4-0.991Ta1^4
Tfil = [111.11(Ta2^4-0.991Ta1^4)]^0.25 = 579.65 K