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` .

Explanation

i) Thermal resitance of aluminium cube, `R_(1) = l/KA`
or `R_(1)=(3.0 xx 10^(-2))/(237)(3.0 xx 10^(-2))^(2)`
`0.14 KW^(-1)`
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)`
Aw these two resistance are in paralle, their equivalent resistance will be
`R=(R_(1)R_(2))/(R_(1)+R_(2))= ((0.14)(0.08))/(0.14) + (0.08) = 0.05 KW^(-1)`
`therefore` Thermal current, H= ("Temperature difference")/("Thermal resistance")`
`(100-20)/(0.05) = 1.6 xx 10^(3)`W
ii) Parallel, thermal current distributing 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`