This might be a lot of work and a lot of explaining but I need help creating an energy system diagram like the example below and writing a reasoning summary to explain the final answer to my big question.

A new "diet" Phenomenon

Your friend Trent is excited about physics because they have discovered they can eat all the shave ice they want without gaining any weight. He says, “I can put just the right amount of flavored syrup on the ice such that I don’t gain any net energy in the process.” You, being a PHYS 2A student, are skeptical and decide to check it out for yourself. You’ll need to model “eating” the shave ice. All the information you need to answer this question can be found here, on the Maybe Useful Information page. 

The Big Question you are trying to answer is: Do you agree or disagree with Trent’s claim: “I put just the right amount of flavored syrup on the ice such that I don’t gain any net energy in the process.” 

Your task is to answer the Big Question in the form of an argument using the Claim, Evidence, Reasoning framework. To do this, you will need to model "eating" the shave ice to come up with a quantitative prediction of the energy gained/released during the process of "eating." Be sure to include any relevant annotations, assumptions, graphical representations, and algebraic representations to support your argument. Below are some questions / prompts to help in case you get stuck.

Guiding Questions / Prompts:

Note, you do not need to answer these questions explicitly (i.e. provide a list of answers). However, your overall solution should demonstrate you know all the answers.

1. What is the Big Question asking? What does “net energy gain” mean? 
2. What is shave ice? Is it similar to any substance we have worked with before? Are there any assumptions we can make about it to make the problem simpler? 
3. How do you “eat” shave ice? (i.e. what do you do with it, where does it go? ). Tell a story about what happens to the shave ice.
4. What representation will help you tell this story? Can you add any information about the beginning and / or end?
5. “Eating” can be complex (the reason I keep putting the word "eat" in quotes is because you are creating a model of "eating" which will require ignoring some processes)! How can we model the scenario in the simplest way possible? Remember, we want to tell the story of the shave ice. Are there any assumptions that will simplify the scenario? Can you ignore chewing? How are you interacting with ice?
6. Keep telling the story of the shave ice as you “eat” it. What do you know about the final state? Can you figure out the final phase and / or temperature? Again, are there any assumptions you can make to simplify the scenario?
7. What representation(s) can help you figure out the amount of energy gained/released when "eating" a single serving of shave ice?
8. What does your final quantitative answer mean? How will you answer the Big Question based on your evidence?

Milestone 1 Maybe Useful Information

Did you know that the "Calorie" count listed on food is actually a unit of energy?  Be careful if you look up the conversion from Calories to kilojoules, because the food Calorie (capitalized) is actually short for a physics kilocalorie (uncapitalized).  The correct conversion for food Calories is:

1 Calorie = 4.184 kJ

In this problem, you should treat food caloric energy as just another sort of energy. 

Below is a nutrition label for a single serving of shave ice. Notice a single serving is listed as 60mL.

Ooops! I made a mistake, the 60mL on the nutrition label only refers to the amount of syrup that goes on your Shave Ice BUT we care what happens to the ice part of the Shave Ice. A typical serving of Shave Ice has a volume of 240mL shaved ice. Please use the volume of the ice (240mL) instead of 60mL (of the syrup). Please check the PHYS 2A announcements as I will have more to say there. Note, there was also a typo in the unit conversion shown below. I have crossed out the 60mL and replaced it 240mL AND converted it correctly this time.

This is a volume, VV, not a mass. You can convert volume to mass if you know the density ρρ (Greek letter "rho", rhymes with "low") of your substance. Density has units of [kgm3][kgm3]. Therefore, to find mass from density:

m=ρVm=ρV

What substance can you model shave ice as (hint you may make assumptions as long as you state and justify them)? Can you look up its density?

Is there a way you can determine mass from the volume of  60mL (0.06L = 0.0000006m³ )  240mL (0.00024m³) once you determine what substance to model the shave ice as?