Question 977: Thermodynamics & KTG

Question

Two rods one made of copper and other made of steel of same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are 385 J s$$-$$1 K$$-$$1 m$$-$$1 and 50 J s$$-$$1 K$$-$$1 m$$-$$1 respectively. The free ends of copper and steel are held at 100$$^\circ$$C and 0$$^\circ$$C respectively. The temperature at the junction is, nearly :

Accepted Answer

We know in conduction, rate of flow of heat $$q = {{ - K.A.\Delta T} \over {\Delta x}}$$
As it is a case of steady state heat transfer
$$ \Rightarrow {{ - {K_{cu}} 	imes A 	imes [100 - {T_j}]} \over l} = {{ - {K_{steel}} 	imes A 	imes [{T_j} - 0]} \over l}$$
Where T
j
is temperature of the junction
$$ \Rightarrow 385(100 - {T_j}) = 50({T_j})$$
$$ \Rightarrow {{100} \over {{T_j}}} - 1 = {{50} \over {385}} \Rightarrow {{100} \over {{T_j}}} = 1 + {{50} \over {385}} \Rightarrow {{100} \over {{T_j}}} = 1.1298$$
$$ \Rightarrow {T_j} = 88.5^\circ C$$

Answer

$$88.5^\circ C$$

Answer

$$12^\circ C$$

Answer

$$50^\circ C$$

Answer

$$73^\circ C$$

Thermodynamics & KTG

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