Question

In a steady state of thermal conduction, temperature of the ends A and B of a 20 cm long rod are 100^(@)C and 0^(@)C respectively. What will be the temperature of the rod at a point at a distance of 6 cm from the end A of the rod

Answer 1

temperature of the rod at a point at a distance 6cm from the end A of the rod is 70°C

It has given that, In a steady state of thermal conduction, temperatures of the ends A and B of a 20cm long rod 100°C and 0°C respectively.

we have to find the temperature of the rod at a point at a distance 6cm from the end A of the rod.

using formula, dQ/dt = KA dT/dx

in steady state of thermal conduction,

dT/dx = constant.

⇒(T₂ - T₃)/x = (T₃ - T₁)/y [see figure. ]

here, T₂ = 100°C , T₁ = 0°C, T₃ = T°C, x = 6cm and y = 20 - 6 = 14 cm

⇒(100 - T)/6 = (T - 0)/14

⇒7(100 - T) = 3T

⇒700 = 10T

⇒T = 70°C

therefore, the temperature of the rod at a point at a distance 6 cm from the end A of the rod is 70°C.