Temperature Control and Chocolate Sculptures

Temperature Control and Chocolate Sculptures
A chocolate artist wants to create small chocolate sculptures that can be purchased as gifts for special occasions. She will create the sculptures in a temperature-controlled room within her chocolate shop. Controlling the temperature of the room is necessary because the visual appearance of chocolate can change if it is heated or cooled outside of a specific temperature range. For example, if the chocolate rises above 18°C, the sculpture may begin to melt and change shape. If the chocolate drops below 15°C, the sculpture may begin to discolor as sugar in the chocolate crystallizes and rises to the surface.

The artist wants to design a box to transport the chocolate sculptures when they are delivered. The chocolate shop is located in a city where the temperatures range between 22°C and 30°C all year long. The temperature inside the delivery van is 20°C. The ideal box will be temperature-controlled using a pack that she will design. The pack will hold a chemical substance and 100 grams of water in separate parts of the pack. Squeezing the pack will combine the two substances, causing a chemical reaction to take place that absorbs or releases energy, depending on the substance. The packs will be activated and added to the insulated box and the chocolate sculpture when it is ready to be transported. The box to transport the chocolate sculptures is shown.

The chocolate artist purchases four different substances: ammonium nitrate, calcium chloride, sodium acetate, and sodium hydroxide. She will test the effects of each substance by adding various amounts to the 100 grams of water, then choose one to create the temperature-control packs. The initial temperature of the water before adding the substance is 20° Celsius. The table shows how much the temperature increased or decreased for each substance. A negative (-) in front of the temperature change indicates a decrease in temperature, and a positive (+) indicates an increase. The artist knows that the kinetic energy of the solution decreases as the temperature decreases.

Substance 10 g 20 g 30 g 40 g 50 g
ammonium nitrate -3 -6 -10 -14 -17
calcium chloride +11 +17 +24 +30 +35
sodium acetate -1 -2 -3 -4 -7
sodium hydroxide +12 +20 +29 +35 +41
Multiple Choice Question
The chocolate artist creates a temperature-control pack to transport her chocolate. She tests the pack while transporting a chocolate sculpture on a very hot day. She finds that the temperature inside of the box is still within the desired range if the trip lasts only one hour. However, if the trip lasts for two hours, the temperature inside of the box is too hot. Which update to the design can the chocolate artist make for longer trips?

A.
She can make a larger temperature-control pack using less of the same chemical.

B.
She can make a smaller temperature-control pack using less of the same chemical.

C.
She can add a second temperature-control pack that is identical to the first pack to the box.

D.
She can add a second temperature-control pack with the coldest possible temperature to the box.

1 answer

To determine the best option for the chocolate artist to ensure that the temperature inside the box stays within the desired range during longer trips, we should consider the information provided about the effectiveness of the temperature-control packs.

Since the artist's initial test results indicate that the temperature within the box remains acceptable for one hour, but becomes too hot after two hours, this suggests that the current temperature-control pack is not sufficient for extended trips.

Now, let's analyze the options:

A. She can make a larger temperature-control pack using less of the same chemical.

  • This option does not seem effective because using less chemical in a larger pack might not provide sufficient cooling or heating capacity.

B. She can make a smaller temperature-control pack using less of the same chemical.

  • This option would likely reduce the cooling/heating capacity further, making it more difficult to maintain the temperature range.

C. She can add a second temperature-control pack that is identical to the first pack to the box.

  • This would double the cooling/heating capacity, which would likely be effective in keeping the temperature stable for a longer period.

D. She can add a second temperature-control pack with the coldest possible temperature to the box.

  • While this sounds effective, the term "coldest possible temperature" is vague and may not be practical or efficient. The effectiveness would depend on the specific substance used and its characteristics.

Considering efficacy and practicality, C is the best option. Adding a second identical temperature-control pack should provide enough additional cooling capacity to maintain the desired temperature range during longer trips.

So, the best update to the design for longer trips is:

C. She can add a second temperature-control pack that is identical to the first pack to the box.