Question 82: Thermodynamics & KTG

Question

A compound slab is made of two parallel plates
of copper and brass of the same thickness and
having thermal conductivities in the ratio 4 : 1.
The free face of copper is at 0$$^\circ$$C. The
temperature of the interface is 20$$^\circ$$C. What is
the temperature of the free face of brass?

Accepted Answer

Given, $${K_{copper}}:{K_{brass}} = 4:1$$
$$ \Rightarrow {{{K_{copper}}} \over {{K_{brass}}}} = {4 \over 1}$$
Let the temperature of the free surface of brass = $$	heta$$
Rate of flow of heat will be equal in both the plates as connected in series.
i.e. $$H = {K_{brass}}{{A(	heta  - 20)} \over l} = {K_{copper}}{{A(20 - 0)} \over l}$$
$$ \Rightarrow {{	heta  - 20} \over {20}} = {{{K_{copper}}} \over {{K_{brass}}}} = {4 \over 1}$$
$$ \Rightarrow 	heta  - 20 = 80$$
$$	heta  = 100\Upsilon C$$

Answer

0$$^\circ$$C

Answer

20$$^\circ$$C

Answer

40$$^\circ$$C

Answer

100$$^\circ$$C

Thermodynamics & KTG

A compound slab is made of two parallel plates of copper and brass of the same thickness and having thermal conductivities in the ratio 4 : 1. The free face of copper is at 0$^\circC. The temperature of the interface is 20^\circ$C. What is the temperature of the free face of brass?

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