Two metal cubes with 3 cm- edges of copper and aluminium are arranged as shown in figure. Find
(a)the total thermal current from one reservoir to the other
(b) the ratio of the thermal current carried by the copper cube to that carried by the aluminium cube. Thermal conductivity of copper is 401 `W//m-K` and that of aluminium id 237 `W//m-K` .

Answer

A, B, C, D

Explanation

(a) Thermal resistance of aluminium cube, `R_1 = l/(KA)`
or `R_1 = (3.0 xx (10^-2))/((237)(3.0 xx 10^-2)^(2))`
`= 0.14 K//W`
and thermal resistance of copper cube, `R_2 = l/(KA)`
or ` R_2 = (3.0 xx 10^-2)/((401)(3.0 xx 10^-2)^2) = 0.08 K//W`
As these two resistance are in parallel, their equivalent resistance will be
`R= ((R_1R_2)/(R_1+R_2))`
`= ((0.14)(0.08))/((0.14)+(0.08))`
`=0.05 K//W`
`:.` Thermal current, `H = ("Temperature difference")/("Thermal resistance")`
`= ((100 -20)/0.05) = 1.6 xx (10^3)W`
(b) In parallel thermal current distributes in the inverse ratio of resistance. Hence,
`H_(Cu)/H_(Al) = (R_(Al)/R_(Cu)) = R_1/R_2 = 0.14/0.08 = 1.75` .