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By Colin Slade

By Colin Slade. alphabet soup. the known stuff. Steel Can D = .066 m t = .001 m T = 20 ºC k Steel = 40 W/m-K. 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. Alphabet Soup D = .064 m H = .093 m m = .305 kg

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By Colin Slade

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  1. By Colin Slade

  2. alphabet soup

  3. the known stuff • Steel Can • D = .066 m • t = .001 m • T = 20 ºC • kSteel = 40 W/m-K • Lighter • D = .02 m • t = .001 m • T = 50 ºC • kNichrome = 11.3 W/m-K • cp Nichrome = 450 J/kg-K • Nichrome = 8400 kg/m3 • Alphabet Soup • D = .064 m • H = .093 m • m = .305 kg • ksoup = .643 W/m-K • cp soup = 4186 J/kg-K • soup = 997 kg/m3 • Tdone = 40 ºC

  4. 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.

  5. calculations • Resistances of the Can and the Soup Rcan = t/ksteelA = .007 W/K Rsoup = H/ksoupA = 45 W/K Rtotal = Rcan +Rsoup = 45.007 W/K • Heat provided by the lighter qconduction = mcp NichromeT T = Tlighter - Tcan = 30 C m = V = At = .003 kg qconduction = 35.6 W • Time required to cook the alphabet soup Modified Lumped Capacitance using Rtotal t = cp V Rtotal ln(Tlighter - Tcan / Tlighter - Tdone) V = m = .305 kg t = 63128 s = 1052 mins = 17 hours

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

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