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Question:

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures T1=300K and T2=100K. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are K1 and K2 respectively. If the temperature at the junction of the two cylinders in the steady state is 200K, then K1/K2=____.

Solution:

We have in steady state, Using Junction rule, i1+i2=0

(\frac{200-100}{L}k_1\pi r^2 + \frac{200-300}{L}k_2\pi (2r)^2 = 0)

(\implies k_1\pi r^2 \times 100 = 100 k_2\pi \times 4r^2 \implies \frac{k_1}{k_2} = 4)