Two cylinders P and Q have the same length and diameter and are made of different materials having thermal conductivities…..

Q: Two cylinders P and Q have the same length and diameter and are made of different materials having thermal conductivities in the ratio 2 : 3. These two cylinders are combined to make a cylinder. One end of P is kept at 100° C and another end of Q at 0°C. The temperature at the interface of P and Q is

(a) 30°C

(b) 40°C

(c) 50°C

(d) 60°C

Solution : (b) Let temperature at interface is θ

k₁(100-θ) = k₂(θ-0)

Here , k₁/k₂ = 2/3

By solving , θ = 40°C