Express the total amount of heat stored in the bar as a

Question

A bar of glass (k = 0.0036 cm²/sec, c_p = 0.39 calories/cm³ °C) 20 cm long is ini­tially at a temperature of 100°C and its ends are maintained at 0°C for t > 0. If the cross section of the bar has area 1 cm², express the total amount of heat stored in the bar as a function of time, and then show that

(i) after five hours the amount of heat remaining in the bar is approximately 16.38% of the amount initially stored,

(ii) if the bar were made of steel (k = 0.128 cm²/sec, c_p = 0.858 calories /cm³ °C), then the amount of heat initially stored in it is more than double the amount initially stored in the glass bar, and

(iii) it takes less than 13 minutes for the amount of heat remaining in the steel bar to equal the amount remaining in the glass bar at the end of five hours.