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 surfaces of spheres of varying radii, all maintained at the same temperature. If Q ∝ R n , where R is the radius, then the value of n is

Question

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 surfaces of spheres of varying radii, all maintained at the same temperature. If Q ∝ R n , where R is the radius, then the value of n is, 2, 1, - 1, - 2

MARKS App · Accepted Answer

Temperature difference causes heat to flow. So, potential difference is equivalent to temperature difference. As, d V d R = - E = - k Q R 2 We can write for heat flux, d T d R = - k Q R 2 Here, Q = heat transferred. ⇒ Q ∝ R 2 when d T δ R = constant. ∴ n = 2

Heat flow	Electrostatics
$T (r)$	$V (r)$
$j (r)$	$E (r)$

Search any question & find its solution

Looking for more such questions to practice?