An ice cream maker is in the form of a soccer ball (Figure P20.71). You fill the inner container with a mixture of cream and sugar at \(32.0^{\circ} \mathrm{C}\) and add rock salt and ice to the sleeve encircling the inner container. You then put both lids on and kick the ice cream maker around like a regular soccer ball until the internal temperature is low enough \(\left(-3.00{ }^{\circ} \mathrm{C}\right)\) to freeze the cream-sugar mixture into ice cream.

(a) If the specific heat capacity of the mixture is \(2900 \mathrm{~J} / \mathrm{K} \cdot \mathrm{kg}\), what quantity of thermal energy must be removed from the inner container to bring \(0.500 \mathrm{~kg}\) of the mixture to the temperature required for freezing?

(b) If the mass of the maker plus its contents is \(3.80 \mathrm{~kg}\), how high above ground level would you need to lift the unit in order for the gravitational potential energy of the ice cream maker-Earth system to be equal to the quantity of energy you found in part \(a\) ?

Data from Figure P20.71

Transcribed Image Text:

outer lid- inner lid- ice cream mixture rock salt and ice