Question

Two metal cubes with $3\text{cm}$ edges of copper and aluminium are arranged as shown in the figure. The total thermal current from one reservoir to the other will be
$(\text{Thermal conductivity,}{K}_{Cu}=385\text{W/m-K},K_{Al}=209\text{W/m-K})$

• A. $1426\text{W}$
• B. $1526\text{W}$
• C. $1626\text{W}$
• D. $1726\text{W}$

Answer 1

The correct option is A $1426\text{W}$

Here, two metal cubes of copper and aluminium are arranged in parallel.
The net thermal current crossing from one reservoir to other will be sum of thermal currents through cubes.

Or, $i_{\text{net}}=i_1+i_2$

$\Rightarrow i_{\text{net}}=\frac{K_{Al}A\Delta T}{L}+\frac{K_{Cu}A\Delta T}{L}$

$\Rightarrow i_{\text{net}}=\frac{A\Delta T}{L}[K_{Al}+K_{Cu}]$

$\Rightarrow i_{\text{net}}=\frac{(9\times {10}^{-4})(100-20)}{3\times {10}^{-2}}[209+385]$

$\Rightarrow i_{\text{net}}\approx 1426\text{W}$

Why this question? Tips: Apply Kirchhoff's Junction rule for thermal current.