Question

A window of a car is found to be covered with 1.3cm of ice. If the area of the window is 1 m2, and the ice is at -12 degrees Celsius, what is the minimum heat required to melt all the ice? Take the density of ice to be 900 kg/m3, the specific heat capacity of ice to be 0.5 cal/g*K, and the latent heat of fusion to be 80 cal/g. Answer in kcal.

Answer 1

Find the volume of the ice:

$$V=Ab.$$

The mass of ice:

$$m=\rho V.$$

The heat to melt it consists of heat required to heat it to melting point (0°) and heat of fusion:

$$Q=Q_1+Q_2,\\ Q=cm(t_f-t_i)+m\lambda=m[c(t_f-t_i)+\lambda],\\ Q=\rho Ab[c(t_f-t_i)+\lambda]=100620\text{ kcal}.$$