$5\mathrm{.}33$ As noted in Problem $5\mathrm{.}3,$ microwave ovens operate by

rapidly aligning and reversing water molecules within

the food, resulting in volumetric energy generation and,

in turn, cooking of the food. When the food is initially

frozen, however, the water molecules do not readily

oscillate in response to the microwaves, and the volu$-$

metric generation rates are between one and two orders

of magnitude lower than if the water were in liquid

form. $($Microwave power that is not absorbed in the

food is reflected back to the microwave generator,

where it must be dissipated in the form of heat to pre$-$

vent damage to the generator.$)$

$($a$)$ Consider a frozen, $1-kg$ spherical piece of ground

beef at an initial temperature of $T_i=-20C$ placed

in a microwave oven with $T_{}=30C$ and $h=$

$15\frac{W}{m^2}*K.$ Determine how long it will take the

beef to reach a uniform temperature of $T=0C,$

with all the water in the form of ice. Assume the

properties of the beef are the same as ice, and

assume $3\%$ of the oven power $(P=1kW$ total$)$ is

absorbed in the food.

$($b$)$ After all the ice is converted to liquid, determine

how long it will take to heat the beef to $T_f=80C$

if $95\%$ of the oven power is absorbed in the food.

Assume the properties of the beef are the same as

liquid water.

$($c$)$ When thawing food in microwave ovens, one may

observe that some of the food may still be frozen

while other parts of the food are overcooked.