please provide clear solution for this A bar 020m in length

please provide clear solution for this

A bar 0.20m in length and of cross- section area 2.5 times 10^-4m^2 is ideally lagged. One end is maintained at 373K while the other is maintained at 273K by immersion in melting ice. Calculate the rate which the ice melts owing to the flow of heat along the bar. Thermal conductivity of the material of the bar =4.0 times 102Wm^-1 K^-T and the specific latent of fusion of ice = 3.4 times 105JK^-1

Solution

Heat transfer rate in the bar is given by the Fourier\'s law of heat conduction as

Q = - K A dT/dx

K = thermal conductivity of the material of the bar

A = Cross sectional area of the bar

dT/dx = Temperature gradient along the length of the bar in the direction of heat flow

Note that negative sign indicates that the temperature decreases in the direction of heat flow as heat flows from a body at high temperature to a body at low temperature.

===> Q = K A (T₁ - T₂)/L at steady state heat transfer

===> Q = 400 W m^-1 K^-1 * 2.5 * 10^-4 m² * (373 - 273) K / 0.2m

===> Q = 50 W

This rate of heat is transferred to the ice at 273 K and it starts to melt.

Rate of heat transfer to melt the ice at the rate of m kg/s is given by

Q = m * L

m = Rate of melting of ice in kg/s

L = Specific latent of fusion of ice = 3.4 * 10⁵ J kg^-1

===> Q = 50 W = m kg/s * 3.4 * 10⁵ J/ kg

===> m = 1.471 * 10^-4 kg/s or 0.1471 grams/second

The rate at which ice melts owing to the heat flow from the bar is m = 0.1471 grams per second