Question

7) a) What is the energy emitted in 1 minute from a black coffee mug which has a radius of 4 cm and height 6 cm and temperature of 70 Fahrenheit. What will the answer be if the coffee mug is at 200 Fahrenheit?

b) Now, assume the mug is completely filled with creamed coffee. Assume both of their temperatures are initially at 200 Fahrenheit and the atmospheric temperature is 70 Fahrenheit. How long will it take each one to reach 71 F ignoring the transfer of heat to each other by conduction? (Take the density of the coffee to be 1.1 g/cm3 , its specific heat to be .95 cal/g.C and the mass of the cup to be 200 grams and its specific heat to be .4 cal/g.C. Also, take the emissivity of the creamed coffee to be .3)

Answer 1

According to Stefan's Law :

the rate of heat energy emmited = [where e = emissivity, A = surface area = T = temperature in Kelvin]

a) t = 1 min = 60 s

e = 1 for black body

T = 70 ^oF = 294.261 K

A =

therefore,

energy emitted = [answer]

if the temperature is 200 ^oF = 366.483 K,

energy emitted = [answer]

b) m = mass of cup = 200 g

M = mass of coffee = V * density =

s = specific heat of coffee = .95 cal/g.C = 3.99 J/g/C

S = specific heat of cup = .4 cal/g.C = 1.68 J/g.c

area of coffe exposed to surrounding =

According to rate law of cooling :

for cup time taken to lower temperature from 200 F to 70 F or change in temperature is 327.039 K is

= 3.40 hr [answer]

for coffee time taken to lower temperature from 200 F to 70 F or change in temperature is 327.039 K is

=133.42 hr [answer]