Charge up timescale given by heat capacity times

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online