Two metal cubes A and B of same size are arranged as shown in the… - Vidyadip

MCQ

Two metal cubes $A$ and $B$ of same size are arranged as shown in the figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of $A$ and $B$ are $300\;W/m{\;^o}C$ and $200\;W/m{\;^o}C$, respectively. After steady state is reached, the temperature of the interface will be...... $^oC$

A
$45$
B
$90$
C
$30$
✓
$60$

✓

Answer

Correct option: D.

$60$

d
(d) Temperature of interface $T = \frac{{{K_1}{\theta _1} + {K_2}{\theta _2}}}{{{K_1} + {K_2}}}$

$ = \frac{{300 \times 100 + 200 \times 0}}{{300 + 200}} = 60^\circ C$

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