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In a steady state, the temperature at the end A and end B of a 20 cm long rod AB are $100^{0} C$ and $0^{0} C$ . The temperature of a point, 12 cm from A is_______

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$50^{0} C$

$45^{0} C$

$40^{0} C$

$65^{0} C$

answer is A.

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Detailed Solution

$l = 20 c m, T_{A} = 100^{0} C,$

$T_{B} = 0^{0} C, T_{9} = ?$

$\frac{d θ}{d t} = \frac{k A Δ θ}{I}$

$\to \frac{K A (100 - 0)}{20} = \frac{K A (100 - T)}{12}$

$300 = 500 - 5 T$

$5 T = 200$

$T = 40^{0} C$

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