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To solve for the steady-state temperature everywhere, you need to solve the heat equation: $$\frac{\partial T}{\partial t} - \chi \nabla^2 T = \frac{S}{c_p \rho}$$ Here, $\chi$ is the thermal diffusivity of the sphere in question, which is defined as the ratio $\kappa / c_p \rho$ (ratio of thermal conductivity to product of specific heat capacity and ...

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When something feels cold, it isn't the temperature that makes it feel cold, it's the rate of heat transfer (heat flux) from your body to the object. Consider that thermal conduction follows Fourier's Law, $\dot{q} = -k A \Delta T$ We can simplify this equation for our purposes by taking one of the objects to be our body, at body temperature, 37$^\circ$C, ...

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I would say that the textbook is using some pretty vague terms here, although I imagine it's simply to make it easier for you to understand. Different materials have different specific heat capacities, a property which indicates how much heat is required to raise the temperature of the material by 1 deg Celcius per gram of the material. For example, the ...

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The metal rod will become hotter. Only not very much for a large rod. The energy will flow from your fingers to the metal until the temperature of the metal reaches the temperature of your fingers. For a large metal object this will never happen for all practical purposes. For a small object, though, it does happen. If you pick up a dime it will ...

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Turns out the reduced electrical conductivity ruins this idea. I've posted my solution here: http://externalcombustion.org/spherical-leads-offer-no-improvement/ Actually a little more inspection shows that there is a small improvement if (and only if) you use larger diameter sphere leads and optimize the cutoff ratio. So it doesn't look like a complete ...

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