Question

A metallic rod 1.5m long and 2×10⁴ m² in area is heated at one end. The coefficient of thermal conductivity of the material of the metallic rod is 210 Js^-1m^-1K^-1 . In the steady-state the temperature of the ends of the rod are 373K and 263 K. Calculate. 

1. Temperature gradient In the rod. 

2. Temperature at a point 0.8 m from the hot end. 

3. Rate of heat transmission.

Answer 1

d =1.5m,

A = 2 × 10⁴m²,

K = 210 W/m/k, θ₁ = 373K and θ₂ = 263K

1. Temperature gradient

2. Let θ be the temperature at a distance d¹ = 0.8m from the hot end then temperature gradient = \(\frac{θ_1-θ }{d^1} \)

i.e., 73.33 = \(\frac{373-θ}{0.8}\) or θ = 314.336 K.

3. Rate of heat transmission

\(\frac{q}{t} =KA \frac{θ_1-θ_2}{d} \)

= 210 × 2 × 10^-4 × 73.33

= 3.08 J/s.