1. During the beer making process, malt (a combination of germinated barley, wheat,

and oats) is soaked with water for some time. The resulting liquid after the soak is

called a wort. The wort is then brought to a boil, during which various sugars and

hops are added. The boiling process typically lasts 1 hour during which approximately

10% of the wort (by mass) is evaporated. Anna, Bob, and Carl decide to hold brewing

competition to determine who can brew beer using the least amount of energy. Each

competitor starts with 0.04 m³ of wort at 20°C. They each use a brewing kettle (surface

area 0.5 m²) opened to the atmosphere (i.e. pressure is constant at 1 atm), and an

immersion heater as a means of adding energy to their wort.

(a) Anna decides to brew an IPA in her kitchen, where the room temperature is 20°C

and the heat transfer coefficient is 5 W/m²-K.

(b) Bob, who has not taken a thermodynamic class, decides to brew a lager outside

during the winter, where the temperature is 0°C and the heat transfer coefficient

is 40 W/m²-K.

(c) Carl spends lots of time and energy perfectly insulating his kettle to brew a stout.

Determine how much electrical energy (in kJ) each contestant requires to brew their

beer. Assume the specific gravity of wort is 1.05, the specific heat capacity of wort

is 3.2 kJ/kg-K, and the heat of vaporization of wort is approximately 92% that of water.

Hint: the heat transfer during a process in which the surface temperature is not

constant can be approximated by Q = hA(Tavg Too), where Taug is the average

temperature between the initial and final state.

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