PHYSICS In steady state heat conduction, the equations that determine the heat current J^{\to}( r^{\to}) [heat flowing per unit time per unit area] and temperature T(r^{\to}) in space are exactly the same as those governing the electric field E^{\to}(r^{\to}) and electrostatic potential V(r^{\to}) with the equivalence given in the Table below : Heat flow Electrostatics T(r^{\to}) V(r^{\to}) J^{\to}(r^{\to}) E^{\to}(r^{\to}) We exploit this equivalence to predict the rate Q of total heat flowing by conduction from the surface of spheres of varying radii, all maintained at the same temperature. If Q \propto R^n , where R is the radius, then the

KVPY SX SB Exam 2018 Question Paper

Question : 91 of 120

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PHYSICS

In steady state heat conduction, the equations that determine the heat current

J↖{→}( r↖{→})

[heat flowing per unit time per unit area] and temperature

T(r↖{→})

in space are exactly the same as those governing the electric field

E↖{→}(r↖{→})

and electrostatic potential

V(r↖{→})

with the equivalence given in the Table below :

Heat flow	Electrostatics
$T(r↖{→})$	$V(r↖{→})$
$J↖{→}(r↖{→})$	$E↖{→}(r↖{→})$

We exploit this equivalence to predict the rate Q of total heat flowing by conduction from the surface of spheres of varying radii, all maintained at the same temperature. If

Q ∝ R^n

, where R is the radius, then the

2
1
-1
-2

Validate

Solution:

We know that

V/E=R

T/J=R;J=T/R

Q/{A×t}=T/R

Q={T×t×A}/R={T×t×4πR^2}/R

Q ∝ R^1

n = 1

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