# If a cup is half full of ice, how long will it take to melt the ice in a microwave oven (1000 W)...

## Question:

If a cup is half full of ice, how long will it take to melt the ice in a microwave oven (1000 W) set on high? Also, if you did the above but added 100ml of ice cold water to the ice would this change the results of melt time?

## Phase Transition

Matter exists in solid, liquid and gaseous phase. In addition to these three most common phases, the matter may go to plasma phase at very high temperature and Bose Einstein condensate state at very low temperature. Transition of matter from one phase to another is associated with energy. Solid phase goes to liquid phase on receiving sufficient energy. During transition all energy given is utilized for transition and temperature of the system remains constant. Once the transition is over temperature will start rising again. Heat energy required for transition depends on mass of the sample and latent heat.

Given data

• A cup half full of ice at zero degree Celsius is kept in the microwave oven.
• The power of the microwave oven {eq}P = 1000 \ W {/eq}
• Latent heat of fusion of ice {eq}L = 3.36 \times 10^5 \ J/kg {/eq}

Let us assume that mass of ice in the cup is {eq}m = 100 \ g {/eq}

Part a)

For melting of one kg ice amount of energy required {eq}Q = m L {/eq}

Therefore time required for melting of ice can be obtained by dividing the heat energy required by power of the oven.

Here we assume no heat loss any where.

Then the time required for melting {eq}t = \dfrac { Q } { P } \\ t = \dfrac { m L } { P } \\ t = 1 \times \dfrac { 3.36 \times 10^5 } { 1000 } \\ t = 336 \ s/ kg {/eq}

Therefore the time required for m = 100 gram {eq}t_1 = t \times 0.100 \\ t_1 = 33.6 \ s {/eq}

Part b)

To the glass in addition to ice at zero degree Celsius 100 ml of water at zero degree Celsius is also added.

This will not change the melting time of ice. Because all the energy given will be utilized for melting of ice and after completion of the melting of ice the temperature will rise.

So no change in temperature until complete melting of ice and time will remain the same for the melting of ice.