Cold Capacity: Exploring the Opposite of Heat Capacity

[Pythagorean]

"cold capacity"

We are taught the notion of heat capacity in undergraduate physics and how different materials can hold a different maximum of heat energy per unit volume.

Is there an opposite notion? Obviously heat is energy, so cold is just lack of it... but my intuition tells me that if I put a big bowl of water in the freezer and let it freeze then, upon power outage, my freezer would stay colder longer than if it was just air in the freezer.

 

[phinds]

I think it's all "heat capacity". Cooling something down is just removing the heat, so it's the heat capacity, just working in reverse. Your bowl of ice WOULD keep the freezer cold longer, but because of its heat capacity in reverse, not a "cold capacity". You have it right that cold is just the absence of heat so you have to treat it all as heat flow, in one direction or another.

 

[Pythagorean]

That makes sense and I think it specifies the confounding point. If it were electrical circuits, I could say "well, the charge/discharge rate depends on the time constant, T = RC". Is it similar in heat, where the resistance to change in temperature, R, is a factor on top of the heat capacity? Or is the heat capacity analogous to electrical capacitance at all? Are there materials that are faster to heat than to cool (or vice versa?)

It seems we ignore the resistance in the undergraduate treatments (it was a long time ago and I was never particularly interested in thermo, so I may be misremembering). The only time I ever dealt with heat resistance was when considering it for insulation in housing and it felt very analogous to ohm's law there, the gradient being like V, the heat resistance, R, and the caloric loss analogous to I.

 

[phinds]

I can't see an analogy to capacitance. As for slow/fast heating/cooling, there are huge differences in speeds among materials. You can dip a copper wire in a candle flame and it grabs the heat so fast the candle goes out. No way would that work with a glass rod, but you can get glass rods REALLY hot if you take the time.

 

[AlephZero]

It seems we ignore the resistance in the undergraduate treatments (it was a long time ago and I was never particularly interested in thermo, so I may be misremembering).

For conduction in solids, the property is "thermal conductivity", which has a good correlation with
electrical conductivity for a wide range of materials (and a quantum mechanics guru could probably explain why). Your "heat capacity" is "specific heat"

But it gets more complicated in fluids because of convection, i.e. local temperature changes cause local density changes, and the non-uniform buoyancy forces move hot and cold bits of the fluid around.
And there is latent heat of fusion and vaporization as well...

Maybe physicists don't find all this so interesting (or relevant in practice) as engineers, but I'm surprised if you never came across Newton's Law of Cooling (which is about convection, not conduction) as an example of a first-order ODE in your basic maths courses.

 

[Chestermiller]

That makes sense and I think it specifies the confounding point. If it were electrical circuits, I could say "well, the charge/discharge rate depends on the time constant, T = RC". Is it similar in heat, where the resistance to change in temperature, R, is a factor on top of the heat capacity? Or is the heat capacity analogous to electrical capacitance at all? Are there materials that are faster to heat than to cool (or vice versa?)

It seems we ignore the resistance in the undergraduate treatments (it was a long time ago and I was never particularly interested in thermo, so I may be misremembering). The only time I ever dealt with heat resistance was when considering it for insulation in housing and it felt very analogous to ohm's law there, the gradient being like V, the heat resistance, R, and the caloric loss analogous to I.

Unlike Phinds, as a guy with lots of heat transfer experience, I definitely can see an analogy between capacitance and heat capacity. The charge on a capacitor is equal to the capacitance times the voltage. The heat stored in a body (say enthalpy or internal energy) is equal to the heat capacity times the temperature (at the simplest level). There is also a resistance concept in heat transfer. This is either the reciprocal of the thermal conductivity divided by thickness, or the reciprocal of the heat transfer coefficient. In heat transfer, a body experiencing transient conductive heat transfer behavior is in many ways analogous to an RC circuit. However, in heat transfer, we are dealing with a spatial distribution of heat capacity and conductivity, rather than discrete resistance and conductance. It is possible, however, to model transient conductive heat transfer using an electric circuit by properly discretizing the heat capacity and conductivity using a sequence of alternating capacitors and resistors.

I might also comment, as a guy with experience in groundwater, that these same concepts of capacitance and resistance apply to groundwater storage, pressurization, and flow in artesian aquifers.

 

[Pythagorean]

I vaguely remember the thermal/electrical conductivity correlation from solid state physics. It probably depends on the particular departments and teachers how interested they are in thermo. The department I was in hired mostly space physicists.

We did Newton's Law of Cooling. But it was more of an exercise in solving the differential equation with boundary conditions and Fourier series solutions than it was about heating/cooling. If I recall, we had a source and a spatial extension and we just looked at the temperature profile. It was over five years ago though. The rest was statistical mechanics (starting with the binomial distribution). I really felt like my thermo exposure was all math with no physics.

 

[Pythagorean]

Unlike Phinds, as a guy with lots of heat transfer experience, I definitely can see an analogy between capacitance and heat capacity. The charge on a capacitor is equal to the capacitance times the voltage. The heat stored in a body (say enthalpy or internal energy) is equal to the heat capacity times the temperature (at the simplest level). There is also a resistance concept in heat transfer. This is either the reciprocal of the thermal conductivity divided by thickness, or the reciprocal of the heat transfer coefficient. In heat transfer, a body experiencing transient conductive heat transfer behavior is in many ways analogous to an RC circuit. However, in heat transfer, we are dealing with a spatial distribution of heat capacity and conductivity, rather than discrete resistance and conductance. It is possible, however, to model transient conductive heat transfer using an electric circuit by properly discretizing the heat capacity and conductivity using a sequence of alternating capacitors and resistors.

Of course. I didn't think of the importance of a spatially extended system vs. the point-system. Which is ironic since modelling neural circuits we often spatially extend circuit models.

 

[atyy]

http://omp.gso.uri.edu/ompweb/doee/science/physical/chtemp6.htm (I think the idea is right, but they should have said specific heat)

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html
http://www.usc.edu/org/cosee-west/Jan292011/Heat%20Capacity%20and%20Specific%20Heat.pdf

Heat capacity C is a constant of proportionality that determines how much heat Q is needed to raise the temperature by 1 unit: Q=C.ΔT

Electrical capacity C is a constant of proportionality that determines how much charge Q is needed to increase the potential difference by 1 unit: Q=C.ΔV

 

[AlephZero]

It is possible, however, to model transient conductive heat transfer using an electric circuit by properly discretizing the heat capacity and conductivity using a sequence of alternating capacitors and resistors.

Time was when people used to get solutions to steady-state two-dimensional thermal problems with the electrical analogy. Cut out the shape of the object from electrically conductive paper, apply voltages and/or currents corresponding the boundary conditions, then probe around with a voltmeter to map out the temperature. The trademark was "teledeltos paper".

The same mathematical idea has reappeared in the finite volume method (not to be confused with the finite element method which is probably more popular). Divide a 3-D object into "small" regions, e.g. blocks or tetrahedra. The math then describes the heat capacity of each block, and the thermal flux flowing through each face between two adjacent blocks.

 

[CWatters]

Obviously heat is energy, so cold is just lack of it... but my intuition tells me that if I put a big bowl of water in the freezer and let it freeze then, upon power outage, my freezer would stay colder longer than if it was just air in the freezer.

No need for the "but" as there isn't a contradiction.

If you change the heat capacity (thermal mass) of the freezer by replacing some of the air with water it will take more energy to raise it's temperature by the same amount.

If the power leaking into the freezer is unchanged it will take longer for the required amount of energy to get in and raise the temperature.

 

[Chestermiller]

Time was when people used to get solutions to steady-state two-dimensional thermal problems with the electrical analogy. Cut out the shape of the object from electrically conductive paper, apply voltages and/or currents corresponding the boundary conditions, then probe around with a voltmeter to map out the temperature. The trademark was "teledeltos paper".

Yes. I remember doing this. We used to call it an analog field plotter.

 

[sophiecentaur]

That makes sense and I think it specifies the confounding point. If it were electrical circuits, I could say "well, the charge/discharge rate depends on the time constant, T = RC". Is it similar in heat, where the resistance to change in temperature, R, is a factor on top of the heat capacity? Or is the heat capacity analogous to electrical capacitance at all? Are there materials that are faster to heat than to cool (or vice versa?)

It seems we ignore the resistance in the undergraduate treatments (it was a long time ago and I was never particularly interested in thermo, so I may be misremembering). The only time I ever dealt with heat resistance was when considering it for insulation in housing and it felt very analogous to ohm's law there, the gradient being like V, the heat resistance, R, and the caloric loss analogous to I.

Thermal resistance can be modeled in the same way as electrical resistance, to some extent but there is a fundamental difference which limits the analogy. When an electrical resistance is introduced into a circuit, energy is transferred (lost ) as heat in the resistance. When 'thermal resistance' is introduced in a heat path, energy is not lost to any other form. There may be energy lost as internal energy in the added layer but that is only transient and, once equilibrium is established, no energy is lost. So the two processes of electrical and thermal conduction may be modeled with the same Maths, they can't be treated as equivalent.