Do blankets commute? Not esthetically (of course), but thermally? Jim Propp
I think they do in the sense that if you have two or more blankets of different thicknesses and materials, and you run the heat equation with boundary conditions that impose two different temperatures on either side, then the flow of heat between them is the same regardless of which order they’re stacked. To put it differently, combining resistors in series is commutative. - Cris
On Dec 5, 2019, at 8:19 AM, James Propp <jamespropp@gmail.com> wrote:
Do blankets commute?
Not esthetically (of course), but thermally?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Cristopher Moore Professor, Santa Fe Institute I confess to an uneasy Physiocratic suspicion, perhaps unbecoming in an academic, that we are throwing more and more of our resources, including the cream of our youth, into financial activities remote from the production of goods and services, into activities that generate high private rewards disproportionate to their social productivity. — James Tobin, 1984
That may be true for conduction and probably radiation but not convection. On Thu, Dec 5, 2019 at 11:29 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I think they do in the sense that if you have two or more blankets of different thicknesses and materials, and you run the heat equation with boundary conditions that impose two different temperatures on either side, then the flow of heat between them is the same regardless of which order they’re stacked. To put it differently, combining resistors in series is commutative.
- Cris
On Dec 5, 2019, at 8:19 AM, James Propp <jamespropp@gmail.com> wrote:
Do blankets commute?
Not esthetically (of course), but thermally?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Cristopher Moore Professor, Santa Fe Institute
I confess to an uneasy Physiocratic suspicion, perhaps unbecoming in an academic, that we are throwing more and more of our resources, including the cream of our youth, into financial activities remote from the production of goods and services, into activities that generate high private rewards disproportionate to their social productivity. — James Tobin, 1984
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I agree - it holds when there is a smooth temperature gradient whose slope depends only on the material. I think this holds fairly well for blankets made of rubber, aluminum, or concrete. - Cris
On Dec 5, 2019, at 12:31 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
That may be true for conduction and probably radiation but not convection.
On Thu, Dec 5, 2019 at 11:29 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I think they do in the sense that if you have two or more blankets of different thicknesses and materials, and you run the heat equation with boundary conditions that impose two different temperatures on either side, then the flow of heat between them is the same regardless of which order they’re stacked. To put it differently, combining resistors in series is commutative.
- Cris
On Dec 5, 2019, at 8:19 AM, James Propp <jamespropp@gmail.com> wrote:
Do blankets commute?
Not esthetically (of course), but thermally?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Cristopher Moore Professor, Santa Fe Institute
I confess to an uneasy Physiocratic suspicion, perhaps unbecoming in an academic, that we are throwing more and more of our resources, including the cream of our youth, into financial activities remote from the production of goods and services, into activities that generate high private rewards disproportionate to their social productivity. — James Tobin, 1984
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But the knit blanket goes under the quilt. On Thu, Dec 5, 2019 at 11:40 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I agree - it holds when there is a smooth temperature gradient whose slope depends only on the material. I think this holds fairly well for blankets made of rubber, aluminum, or concrete.
- Cris
On Dec 5, 2019, at 12:31 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
That may be true for conduction and probably radiation but not convection.
On Thu, Dec 5, 2019 at 11:29 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I think they do in the sense that if you have two or more blankets of different thicknesses and materials, and you run the heat equation with boundary conditions that impose two different temperatures on either side, then the flow of heat between them is the same regardless of which order they’re stacked. To put it differently, combining resistors in series is commutative.
- Cris
On Dec 5, 2019, at 8:19 AM, James Propp <jamespropp@gmail.com> wrote:
Do blankets commute?
Not esthetically (of course), but thermally?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Cristopher Moore Professor, Santa Fe Institute
I confess to an uneasy Physiocratic suspicion, perhaps unbecoming in an academic, that we are throwing more and more of our resources, including the cream of our youth, into financial activities remote from the production of goods and services, into activities that generate high private rewards disproportionate to their social productivity. — James Tobin, 1984
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I understood the question differently. Based on the blankets in my house, blankets do not commute to work or anywhere else, but stay on the coach all day. -Veit
On Dec 5, 2019, at 2:42 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
But the knit blanket goes under the quilt.
On Thu, Dec 5, 2019 at 11:40 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I agree - it holds when there is a smooth temperature gradient whose slope depends only on the material. I think this holds fairly well for blankets made of rubber, aluminum, or concrete.
- Cris
On Dec 5, 2019, at 12:31 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
That may be true for conduction and probably radiation but not convection.
On Thu, Dec 5, 2019 at 11:29 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I think they do in the sense that if you have two or more blankets of different thicknesses and materials, and you run the heat equation with boundary conditions that impose two different temperatures on either side, then the flow of heat between them is the same regardless of which order they’re stacked. To put it differently, combining resistors in series is commutative.
- Cris
On Dec 5, 2019, at 8:19 AM, James Propp <jamespropp@gmail.com> wrote:
Do blankets commute?
Not esthetically (of course), but thermally?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Cristopher Moore Professor, Santa Fe Institute
I confess to an uneasy Physiocratic suspicion, perhaps unbecoming in an academic, that we are throwing more and more of our resources, including the cream of our youth, into financial activities remote from the production of goods and services, into activities that generate high private rewards disproportionate to their social productivity. — James Tobin, 1984
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Evidently the question was coached insufficiently precisely beforehand --- er, or do I mean the questioner .... WFL On 12/5/19, Veit Elser <ve10@cornell.edu> wrote:
I understood the question differently. Based on the blankets in my house, blankets do not commute to work or anywhere else, but stay on the coach all day.
-Veit
On Dec 5, 2019, at 2:42 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
But the knit blanket goes under the quilt.
On Thu, Dec 5, 2019 at 11:40 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I agree - it holds when there is a smooth temperature gradient whose slope depends only on the material. I think this holds fairly well for blankets made of rubber, aluminum, or concrete.
- Cris
On Dec 5, 2019, at 12:31 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
That may be true for conduction and probably radiation but not convection.
On Thu, Dec 5, 2019 at 11:29 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I think they do in the sense that if you have two or more blankets of different thicknesses and materials, and you run the heat equation with boundary conditions that impose two different temperatures on either side, then the flow of heat between them is the same regardless of which order they’re stacked. To put it differently, combining resistors in series is commutative.
- Cris
On Dec 5, 2019, at 8:19 AM, James Propp <jamespropp@gmail.com> wrote:
Do blankets commute?
Not esthetically (of course), but thermally?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Cristopher Moore Professor, Santa Fe Institute
I confess to an uneasy Physiocratic suspicion, perhaps unbecoming in an academic, that we are throwing more and more of our resources, including the cream of our youth, into financial activities remote from the production of goods and services, into activities that generate high private rewards disproportionate to their social productivity. — James Tobin, 1984
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Those aren’t your blankets; that’s your dog.
On Dec 5, 2019, at 1:29 PM, Veit Elser <ve10@cornell.edu> wrote:
I understood the question differently. Based on the blankets in my house, blankets do not commute to work or anywhere else, but stay on the coach all day.
-Veit
On Dec 5, 2019, at 2:42 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
But the knit blanket goes under the quilt.
On Thu, Dec 5, 2019 at 11:40 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I agree - it holds when there is a smooth temperature gradient whose slope depends only on the material. I think this holds fairly well for blankets made of rubber, aluminum, or concrete.
- Cris
On Dec 5, 2019, at 12:31 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
That may be true for conduction and probably radiation but not convection.
On Thu, Dec 5, 2019 at 11:29 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I think they do in the sense that if you have two or more blankets of different thicknesses and materials, and you run the heat equation with boundary conditions that impose two different temperatures on either side, then the flow of heat between them is the same regardless of which order they’re stacked. To put it differently, combining resistors in series is commutative.
- Cris
On Dec 5, 2019, at 8:19 AM, James Propp <jamespropp@gmail.com> wrote:
Do blankets commute?
Not esthetically (of course), but thermally?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Cristopher Moore Professor, Santa Fe Institute
I confess to an uneasy Physiocratic suspicion, perhaps unbecoming in an academic, that we are throwing more and more of our resources, including the cream of our youth, into financial activities remote from the production of goods and services, into activities that generate high private rewards disproportionate to their social productivity. — James Tobin, 1984
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There's also the simple effect of weight. A heavy blanket on top of a light one may compress it and reduce it's thermal resistance. Brent On 12/5/2019 11:42 AM, Tomas Rokicki wrote:
But the knit blanket goes under the quilt.
On Thu, Dec 5, 2019 at 11:40 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I agree - it holds when there is a smooth temperature gradient whose slope depends only on the material. I think this holds fairly well for blankets made of rubber, aluminum, or concrete.
- Cris
On Dec 5, 2019, at 12:31 PM, Tomas Rokicki <rokicki@gmail.com> wrote:
That may be true for conduction and probably radiation but not convection. On Thu, Dec 5, 2019 at 11:29 AM Cris Moore via math-fun < math-fun@mailman.xmission.com> wrote:
I think they do in the sense that if you have two or more blankets of different thicknesses and materials, and you run the heat equation with boundary conditions that impose two different temperatures on either side, then the flow of heat between them is the same regardless of which order they’re stacked. To put it differently, combining resistors in series is commutative.
- Cris
On Dec 5, 2019, at 8:19 AM, James Propp <jamespropp@gmail.com> wrote:
Do blankets commute?
Not esthetically (of course), but thermally?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun Cristopher Moore Professor, Santa Fe Institute
I confess to an uneasy Physiocratic suspicion, perhaps unbecoming in an academic, that we are throwing more and more of our resources, including the cream of our youth, into financial activities remote from the production of goods and services, into activities that generate high private rewards disproportionate to their social productivity. — James Tobin, 1984
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Just as thermal conductors...sure. But not if you take into account things like transfer of latent heat (water vapor) and radiative transfer with the environment (black blanket on top is warmer in the Sun). Brent On 12/5/2019 7:19 AM, James Propp wrote:
Do blankets commute?
Not esthetically (of course), but thermally?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (6)
-
Brent Meeker -
Cris Moore -
Fred Lunnon -
James Propp -
Tomas Rokicki -
Veit Elser