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Unformatted text preview: barely above ambient)
– now the T across the insulation is P ·t/( A c · ) = 9.5°
– so Tin = 30.3° • Notice a few things:
– radiation and convection nearly equal influence (0.617 vs.
0.675)
– shutting off either would result in small (but measurable)
change Winter 2008 18 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 Timescales Heating a lump by conduction • So far we’ve looked at steadystate equilibrium
we’
situations
• How long will it take to “chargeup” the system?
chargeup”
• Timescale given by heat capacity times temperature
change divided by power
– • Heating food from the outside, one relies entirely on
thermal conduction/diffusion to carry heat in
• Relevant parameters are:
–
–
–
– c p·m· T/P • For ballpark, can use cp
anything 1000 J/kg/K for just about
1000 • Just working off units, derive a timescale: – so the box from before would be 2.34 kg if it had the density
of water; let’s say 0.5 kg in truth
– average charge is half the total T, so about 5°
– total energy is (1000)(0.5)(5) = 2500 J
– at 1W, this has a 40 minute timescale
Winter 2008 Lecture 4 thermal conductivity, (how fast does heat move) (W/m/K)
heat capacity, cp (how much heat does it hold) (J/kg/K)
mass, m (how much stuff is there) (kg)
size, R —like a radius (how far does heat have to travel) (m) 19 –
(cp/ )(m /R) 4(cp/ ) R2
– where is density, in kg/m3:
m /((4/3) R3) m /4R 3
– faster if: c p is small, is large, R is small (these make sense)
– for typical food values,
6 minutes (R /1 cm)2
– egg takes ten minutes, turkey takes 5 hours
Winter 2008 20 5 Thermal Considerations 01/17/2008 UCSD: Physics 121; 2008 UCSD: Physics 121; 2008 Lab Experiment Lab Experiment, cont. • We’ll build boxes with a heat load inside to test the
We’
ideas here
• In...
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 Winter '08
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 Energy, Thermal Energy

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