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# How quickly heat transfers through an insulating layer depends on that

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Math Expert
Joined: 02 Sep 2009
Posts: 58005
How quickly heat transfers through an insulating layer depends on that  [#permalink]

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22 Aug 2019, 22:20
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:26) correct 45% (01:21) wrong based on 38 sessions

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How quickly heat transfers through an insulating layer depends on that insulator's thermal resistance. If two insulators are used together, the inverse of the combined thermal resistance is sum of the reciprocals of each layer's thermal resistance. If the thermal resistances of two insulators are r and 2r, what is their combined resistance?

A. 2r^2
B. 3r
C. 1/(3r)
D. 2r/3
E. 3/(2r)

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How quickly heat transfers through an insulating layer depends on that  [#permalink]

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Updated on: 23 Aug 2019, 00:36
Bunuel wrote:
How quickly heat transfers through an insulating layer depends on that insulator's thermal resistance. If two insulators are used together, the inverse of the combined thermal resistance is sum of the reciprocals of each layer's thermal resistance. If the thermal resistances of two insulators are r and 2r, what is their combined resistance?

A. 2r^2
B. 3r
C. 1/(3r)
D. 2r/3
E. 3/(2r)

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1/r+1/2r = 3r/2r^2 ; 3/(2r ; 2r/3)
IMO D;
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Originally posted by Archit3110 on 22 Aug 2019, 22:44.
Last edited by Archit3110 on 23 Aug 2019, 00:36, edited 1 time in total.
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Re: How quickly heat transfers through an insulating layer depends on that  [#permalink]

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23 Aug 2019, 00:32
The sum of the reciprocals. = 1/r + 1/ 2r = 3 / 2r

Which is equal to the inverse of the thermal resistance together

Therefore Thermal resistance = 1 / (3/2r) = 2r / 3 -

IMO D
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Re: How quickly heat transfers through an insulating layer depends on that  [#permalink]

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25 Aug 2019, 21:55
Bunuel wrote:
How quickly heat transfers through an insulating layer depends on that insulator's thermal resistance. If two insulators are used together, the inverse of the combined thermal resistance is sum of the reciprocals of each layer's thermal resistance. If the thermal resistances of two insulators are r and 2r, what is their combined resistance?

A. 2r^2
B. 3r
C. 1/(3r)
D. 2r/3
E. 3/(2r)

Project PS Butler

Given: How quickly heat transfers through an insulating layer depends on that insulator's thermal resistance. If two insulators are used together, the inverse of the combined thermal resistance is sum of the reciprocals of each layer's thermal resistance.

Asked: If the thermal resistances of two insulators are r and 2r, what is their combined resistance?

1/R = 1/r + 1/2r = 3/2r
R = 2r/3

IMO D
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Re: How quickly heat transfers through an insulating layer depends on that   [#permalink] 25 Aug 2019, 21:55
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