Question

can you solve it? figure 18. the worlds largest glutinous rice cake was prepared in china in 2016 by the work of over fifty cooks. imagine the amount of ingredients required to prepare a rice - cake that is almost 4 meters (12.5 feet) in diameter. the bakers of this giant rice cake used over 1300 pounds of rice! packaged foods typically have a nutrition label showing the amount of energy the food contains in a serving. this energy is shown as a number of calories. but how would you determine the number of calories in a certain mass of this food - breaking food such as this cake? what types of equipment would you need, and how would you gather data to determine the amount of energy in this massive amount of food? evidence notebook in your evidence notebook, make a claim for how you could measure the amount of energy contained in this rice cake. use evidence and examples to support your claim, and explain your reasoning. in your explanation, address the following questions: 1. how could a scientist determine the number of calories in a certain mass of this food? 2. how could you determine the number of calories in the entire rice cake if you knew the number of calories in a smaller sample? provide mathematical models in the form of example calculations to illustrate how this could be done. 3. how would the size of the sample tested and the precision of the equipment used affect the number of calories calculated for the whole rice cake?

Explanation:

Step1: Define calorie measurement principle

Calories in food can be measured by calorimetry. The energy released when food is burned is absorbed by a known - mass of water, and the temperature change of the water is measured. The heat absorbed by water $Q = mc\Delta T$, where $m$ is the mass of water, $c$ is the specific - heat capacity of water ($c = 4.18\space J/(g\cdot^{\circ}C)$), and $\Delta T$ is the temperature change.

Step2: Determine calories in a sample

For a small sample of the food, burn it in a bomb calorimeter. First, measure the mass of the sample $m_{sample}$. Then, measure the mass of water $m_{water}$ in the calorimeter and its initial temperature $T_1$. After burning the sample completely, measure the final temperature $T_2$. The heat absorbed by water $Q = m_{water}c\Delta T=m_{water}c(T_2 - T_1)$. The number of calories in the sample $C_{sample}=\frac{Q}{4.18}$ (since $1\space calorie = 4.18\space J$).

Step3: Scale up to whole cake

If the mass of the whole rice - cake is $M$ and the mass of the sample is $m_{sample}$, and the number of calories in the sample is $C_{sample}$, then the number of calories in the whole cake $C_{whole}=\frac{M}{m_{sample}}\times C_{sample}$.

Step4: Consider equipment and data - gathering

Equipment needed includes a bomb calorimeter, a balance to measure the mass of the sample and water, and a thermometer to measure the temperature of water. To gather data, record the mass of the sample, mass of water, initial and final temperatures of water accurately.

Step5: Analyze impact of sample size and equipment precision

A larger sample size will give a more accurate representation of the whole cake's calorie content as it reduces the effect of non - uniformity in the cake. Higher - precision equipment (e.g., a more accurate thermometer and balance) will lead to more precise calorie calculations for the whole cake.

Answer:

1. A scientist can use a bomb calorimeter to determine the number of Calories in a certain mass of the food. Burn the food sample in the calorimeter, and measure the heat absorbed by the surrounding water to calculate the energy content.
2. First, measure the number of Calories in a small sample as described above. Let the mass of the whole cake be $M$ and the mass of the sample be $m_{sample}$, and the number of calories in the sample be $C_{sample}$. Then the number of calories in the whole cake $C_{whole}=\frac{M}{m_{sample}}\times C_{sample}$. For example, if the sample has a mass of 10 g and contains 50 Calories, and the whole cake has a mass of 1000 g, then $C_{whole}=\frac{1000}{10}\times50 = 5000$ Calories.
3. A larger sample size will give a more accurate result as it better represents the whole cake's composition. Higher - precision equipment (more accurate thermometers and balances) will lead to more precise calorie calculations for the whole cake, reducing errors in the measurement of heat transfer and mass.