2. By Colin Slade

3. alphabet soup

4. the known stuff  Lighter  D =.02 m  t =.001 m  T = 50 ºC  k Nichrome = 11.3 W/m-K  c p Nichrome = 450 J/kg-K   Nichrome = 8400 kg/m 3  Lighter  D =.02 m  t =.001 m  T = 50 ºC  k Nichrome = 11.3 W/m-K  c p Nichrome = 450 J/kg-K   Nichrome = 8400 kg/m 3  Steel Can  D =.066 m  t =.001 m  T = 20 ºC  k Steel = 40 W/m-K  Steel Can  D =.066 m  t =.001 m  T = 20 ºC  k Steel = 40 W/m-K  Alphabet Soup  D =.064 m  H =.093 m  m =.305 kg  k soup =.643 W/m-K  c p soup = 4186 J/kg-K   soup = 997 kg/m 3  T done = 40 ºC  Alphabet Soup  D =.064 m  H =.093 m  m =.305 kg  k soup =.643 W/m-K  c p soup = 4186 J/kg-K   soup = 997 kg/m 3  T done = 40 ºC

5. assumptions  The can is inside the car and assumed to be at the same temperature as the quiescent air. Convection, forced and free, can be neglected.  The can does not reach a sufficiently high temperature and radiation can be neglected as well.  Therefore, heat transfer is due only to conduction from the lighter to the can.  The can is inside the car and assumed to be at the same temperature as the quiescent air. Convection, forced and free, can be neglected.  The can does not reach a sufficiently high temperature and radiation can be neglected as well.  Therefore, heat transfer is due only to conduction from the lighter to the can.

6. calculations  Heat provided by the lighter q conduction = mc p Nichrome  T  T = T lighter - T can = 30  C m =  V =  At =.003 kg q conduction = 35.6 W  Heat provided by the lighter q conduction = mc p Nichrome  T  T = T lighter - T can = 30  C m =  V =  At =.003 kg q conduction = 35.6 W  Resistances of the Can and the Soup R can = t/k steel A =.007 W/K R soup = H/k soup A = 45 W/K R total = R can + R soup = 45.007 W/K  Resistances of the Can and the Soup R can = t/k steel A =.007 W/K R soup = H/k soup A = 45 W/K R total = R can + R soup = 45.007 W/K  Time required to cook the alphabet soup Modified Lumped Capacitance using R total t =  c p V R total ln(T lighter - T can / T lighter - T done )  V = m =.305 kg t = 63128 s = 1052 mins = 17 hours  Time required to cook the alphabet soup Modified Lumped Capacitance using R total t =  c p V R total ln(T lighter - T can / T lighter - T done )  V = m =.305 kg t = 63128 s = 1052 mins = 17 hours

7. conclusions  There is no way you could cook a can of soup with a single car lighter. It simply does not produce enough heat.