Two rods having thermal conductivity in the ratio of 5 : 3 having equal lengths and equal cross-sectional area are joined end to end. If the temperature of the free end of the first rod is 100°C and free end of the second rod is 20°C, then the temperature of the jucntion is

We can solve this problem using the formula for heat transfer through a rod, which is as follows:

Q = (kA(T₁ – T₂)) / L

where:
– Q is the heat transferred,
– k is the thermal conductivity,
– A is the cross-sectional area,
– (T₁ – T₂) is the temperature difference,
– L is the length of the rod.

Since the rods are connected end to end, heat transfer by both the rods is identical. The heat transfer by both the rods is the same:

(k₁A(T₁ – T)) / L = (k₂A(T – T₂)) / L

where:
– k₁ and k₂ are the thermal conductivities of the first and second rods,
– T₁ and T₂ are the temperatures at the free ends of the first and second rods
– T is the temperature at the junction.

Given:
– The ratio of thermal conductivity is k₁ : k₂ = 5 : 3,
– T₁ = 100°C,
– T₂ = 20°C.

Now, equating the heat transfer in both rods:

(5(100 – T)) / 3 = (T – 20)

Solving for T:

5(100 – T) = 3(T – 20)

500 – 5T = 3T – 60

500 + 60 = 8T

560 = 8T

T = 70°C

Hence, the temperature at the junction is 70°C.

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