a) You radiate away heat at your T = 301 K clothing temperature. The blaclbody emission rate is
(sigma)*T^4*area
sigma is the Stefan-Boltzmann contstant. Its value is
0.567*10^-7 W/m^2*K^4
(b) Learn about and apply the Wien displacement law.
(peak wavelength)*(Temperature)= 0.290 cm K
(c) Use the blackbody law again, but this time with T = 288K, and the same body aarea
(d) Subtract answer (c) from answer (a)
(e) Energy loss rate * Time = 2*10^6 cal*4.18 J/cal.
Solve for Time
I'd love thorough solutions to these problems, but simply providing the specific formulas that I should solve each part of the problem with would be really good too. :-)
Thanks!
Human energetics
You are sitting down to study in the library. Let’s find out what limits the time you are able to spend studying.
a) Calculate how much power you are radiating, in watts. While your skin temperature is about 33 degrees Celsius, the outside of your clothing is at about 28 degrees Celsius. In the absence of perspiration, black body radiation at this temperature is your main radiation mechanism. You can take your surface area to be 2 m^2.
b) What is the wavelength of the peak of your spectrum? Comment why we cannot see each other in a dark room.
c) Your body is constantly emitting thermal radiation and is also absorbing radiation from the surroundings. The library is unusually chilly today, and the ambient temperature is 15 degrees Celsius. How much power are you absorbing from the room, in watts? You can use the black body formula at the temperature of the room.
d) What’s your net energy loss rate, in watts? Compare this to a typical 60W light bulb. How much energy will you lose per day, in mega-Joules?
e) On a normal dorm diet, your daily energy intake from food should be close to 2000 kilo-calories (kcal), where one calorie is defined as 4.2 Joules. How long will you be able to study in this library before your daily energy intake is exhausted?
1 answer
1 answer