Question

Some ice cubes at 0⁰Cwith a total mass of 403gare placed in a microwave oven and subjected to 750W (750J/s)of energy for 5.00 minutes. What is the final temperature of the water? Assume all the energy of the microwave is absorbed by the water, and assume no heat loss by the water.

Short answer

The final temperature of the water would be 53.7⁰C.

Step-by-step solution

Heat energy absorbed

The amount of heat absorbed by the 403g of ice at 0⁰C is utilized for melting the ice and then increasing the temperature.

$$\begin{gathered} Total heat energy absorbed=power\times time \\ =750J/s\times 300s \\ =22.5\times {10}^{4}J \end{gathered}$$

The heat energy required to melt the ice

The amount of heat required to melt the ice is:

(“q” is heat absorbed, “m”mass of ice, “$∆H$”heat of fusion of ice)

$$\begin{gathered} q=m\Delta H \\ =333.55J/g \\ =403g\times 333.55J/g \\ =13.44\times {10}^{4}J \end{gathered}$$

The final temperature of the water

Therefore, the amount of heat required to raise the temperature = Total energy heat energy absorbed – the amount of heat required to melt the ice

( C = specific heat capacity of water, $\Delta T=T_{final}-T_{initial}$)

$$\begin{gathered} mC\Delta T=\left(22.5\times {10}^4-13.44\times {10}^4\right)J \\ 403g\times 4.184J/g{}^{\circ }C\times \left(T_{final}-0{}^{\circ }C\right)=9.06\times {10}^{4}J \\ {T}_{final}=53.7{}^{\circ }C \end{gathered}$$