04_thermal

# Charge up timescale given by heat capacity times

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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 steady-state equilibrium we’ situations • How long will it take to “charge-up” the system? charge-up” • 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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