Question

A student is doing an experiment using a 200 W heat plate. He is heating a 300 g block of ice at -20°C to water at
20°C. How long will it take?

Answer 1

First, calculate the amount of heat required to increase the ice temperature from -20°C to 0°C:

$$Q_i=mc_i\Delta t_i.$$

Next, calculate the amount of heat required to melt the ice at 0°C:

$$Q_m=mL.$$

Finally, calculate the amount heat required to heat water up from 0 to 20°C:

$$Q_w=mc_w\Delta t_w.$$

As we know, to give the total amount of heat

$$Q=Q_i+Q_m+Q_w$$

to the water is power times time:

$$Q=P\tau,\\ \space\\ \tau=\frac{Q}{P}=\frac{m(c_w\Delta t_w+L+c_i\Delta t_i)}{P}=\\\space\\ =\frac{0.3(4200\cdot20+330000+2108\cdot20)}{200}=684\text{ s},$$

or 11 min 24 s.