A bar 0.2 m in length and 2.5 cm² in cross section is ideally lagged. One end is maintained at 100^oC and the other end is maintained at 0^oC by immersing in melting ice. Calculate the mass of ice melt in one hour. Thermal conductivity of the material of the bar is 4 x 10² Wm^-1K^-1.

Solution

Length of bar (l) = 0.2 m

Cross section area (A) = 2.5 cm² = 2.5 x 10^-4 m²

Temperature of one end [latex](\theta_1)[/latex] = 100^oC

Temperature of other end [latex](\theta_2)[/latex] = 0^oC

Mass of ice melted (m) =?

Time (t) = 1 hour = 60 x 60 = 3600 s

Thermal conductivity of the material of the bar (K) = 4 x 10² Wm^-1K^-1

We know that,

Q₁ = [latex]\frac{KA(\theta_1 – \theta_2)t}{l}[/latex] …………………. (i)

Also, quantity of heat required to melt ice

Q₂ = mL_f ……………. (ii)

According to question,