Three metal rods made of copper, aluminium and brass, each 20 cm long and 4 cm in diameter, are placed end to end with aluminium between the other two. The free ends of copper and brass are maintained at 100 and 0°C respectively. Assume that the thermal conductivity of copper is twice that of aluminium and four times that of brass. The equilibrium temperatures of the copper-aluminium and aluminium-brass junctions are respectively.
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According to the picture that is given in the question, we see that the three rods are connected in series with each other. So the heat current that is flowing through the three rods will be equal to one another. Now according to the question the length and the area of cross-section of all the three rods are the same. So we take them as 
and 
for all the rods. The thermal conductivity of copper is twice that of aluminium and four times that of brass. So we take the thermal conductivity of aluminium as 
. So the thermal conductivity of copper is 
and that of brass is 
Therefore we can use the formula for the heat current through each of the rods as,
On equating the three we have,
Now from 
On cancelling the common terms on both the sides we have,
On taking the similar terms to one side we have,
On adding we have
Now from 
we get,
Again on cancelling the common terms we have,
On opening the brackets and taking common terms to one side we get,
Hence we have,
Now on substituting 
we get,
On subtracting we get,
Hence we get the temperature as,
On calculating this gives us,
This is approximately equal to 
Substituting this value in 
we get,
Hence, 
This is approximately equal to,
So the temperatures are 
and 
.
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