If K 1 and K 2 are the thermal conductivities L 1 and L 2 are the lengths and A 1 and A 2 are the cross sectional areas of steel and copper rods respectively such that K 2 K 1 = 9 , A 1 A 2 = 2 , L 1 L 2 = 2 . Then, for the arrangement as shown in the figure. The value of temperature T of the steel - copper junction in the steady state will be

Step-by-step solution

At steady state, the heat conducted by both the rods will be the same. The rate of heat conduction is given by, d Q d t = K A l ∆ T . Therefore, if the temperature of the junction is T , K 1   A 1 l 1 T 1 - T = K 2   A 2 l 2 T - T 2 ⇒ 450 - T T - 0 = K 2   A 2 l 1   K 1   A 1 l 2 = 9 × 1 2 × 2 ⇒ 450 - T = 9   T ⇒ T = 45 ° C