Question

A uniform slab of dimension 10 cm $\times$ 10 cm $\times$ 1 cm is kept between two heat reservoirs at temperatures ${10}^{\circ }C$ and ${90}^{\circ }C$. The larger surface areas touch the reservoirs. The thermal conductivity of the material is $0.80W{m}^{-1\circ }{C}^{-1}$ Find the amount of heat flowing through the slab per minute.

Answer 1

$T_1={90}^{\circ }C,T_2={10}^{\circ }C$

l = 1 cm = 0.01 m

A = $10cm\times 10cm$

$=0.1\times 0.1m^2=1\times {10}^{-2}{m}^2$

k = $0.80W/m{-}^{\circ }C$

$\frac{Q}{t}=\frac{kA(T_1-T_2)}{l}$

$=\frac{8\times {10}^{-1}\times {10}^{-2}\times (90-10)}{1\times {10}^{-2}}$

= 64 J/s = 3840J/min.