Heat =mass x temperature change x specific heat.
The specific heat capacity of water is 4.18 Joules/gram/oC.
What does this mean? It means if you have some water, in order to heat it up, it will take 4.18 Joules of energy PER each gram of water present PER every degree you are trying to heat it up.
So if you had 100grams of water, and you tried to heat it from 30oC to 40oC (a 10oC change) then it would take 100g x 10oC x 4.18J/g/oC = 4180J (or 4.18KJ) of energy to cause this change.
Side note. 4.18J = 1 calorie. 1000 calories = 1 Kilocalorie (which is technically food Calorie, which is technically capitolized to represent Kilocalorie). So a 1 (food) Calorie mint would have enough energy, if burned, to heat 100g of water 10oC. That is a lot of energy!
Temperature change = (Final temperature – Starting temperature).
Remember that heat is ENERGY. Both are measured in Joules. This means that heat is conserved. Because heat is conserved, there are a number of applications we can do to figure out an unknown. For example, when a certain amount of a substance is burned, we can measure how much a container of water heats up … and this is how calories are measured in food.
However, to understand the equation above well, we’ll start simply with 2 containers of water. We will use different materials later in the class.
Procedure.
Touch some metal and some nonmetal samples from within the same room of your house – obviously, 1 can’t be in the sun and others in the shade.. Which one feels colder? Is it really colder? Test it (you have a thermometer). Explain.
Get samples of hot water and some cold water – while we got the good materials, I would not use boiling hot water. Because the container itself will absorb some heat, it is best if this containers are as light as possible (thus low mass, thus low heat) – styrofoam or paper or plastic cuts. You are (eventually) going to mix them together and see what the final temperature is. Before you mix, look at the formula for heat at the top of the page. What 2 things do you need to measure about EACH sample of water that would help you to predict where the final temperature after mixing should end up? In fact, it is better if you try to control your variables when you can – for example – you have the ability to control the mass of the water you use. Make those 4 measurements, predict the final temperature, mix the water, and record the final temperature. Was the final temperature where you thought it would be? Was it exactly ½ way in between? Why or why not?
Something you have to understand is that the final temperature (after mixing) is the final temperature of both the hot water AND the cold water.
Calculate the heat lost by the hot water, and the heat gained by the cold water. How do these compare? Make sure you discuss this with me.
The heat lost by the hot water would be the (Mass of the hot water) x (the temperature change of hot water) x 4.18 J/g/oC.
The heat gained by the cold water would be the (Mass of the cold water) x (the temperature change of the cold water) x 4.18J/g/oC.
NOTE – the hot and cold water will both move towards room temperature over time… AND the further from room temperature they are, the faster they change. So measure masses of both first. Then temp, then mix.
Repeat the experiment, but this time make your mass of hot water NOT the same as the cold water. Like 2x as much hot as cold (or vice versa). Make any other changes that you pick up from the mistake(s) made in the previous example.
Was the final temperature where you thought it would be? Was it exactly ½ way in between? Why or why not?
Calculate the heat lost by the hot water, and the heat gained by the cold water. How do these compare? Should they be the same? Why or why not?
What can you conclude about heat energy transfer with respect to the law of conservation of energy?
Now we are going to repeat one more time.
(Read the directions and think ahead … you need to have enough hot and cold water to cover the weight and a big enough cup to hold the water and the weight without spilling). This time, put your 200g mass into the hot water. Let it sit for maybe 3 minutes until the temperature levels out (you can tell this if you have your thermometer in it…). Note this temperature.
Then quickly check the temp of the cold water and put the hot mass into the cold water. Stir with the thermometer until the temperature levels out. This is the final temperature of both the weight and the water.
The weight is chrome plated STEEL. Look up the specific heat capactiy of steel in colomn 3 of https://en.wikipedia.org/wiki/Table_of_specific_heat_capacities and use that instead of the 4.18 in the heat equation (since 4.18 is for water).
Calculate the heat lost by the hot weight and the heat gained by the cold water. How do these compare? Should they be the same? Why or why not?
What can you conclude about heat energy transfer with respect to the law of conservation of energy?
Make sure you are not confusing heat (solved by the big formual at the top of the page) and temperature.
As stated above, we can estimate what the “energy” in a piece of food is by measuring how much heat enery is absorbed by some water placed above it. The procedure below should be possible to do in most home settings. You need a snack food (chip, nut – cashews are amazing, cheetos and potato chips work really well too), something to hold the nut or prop it up (tongs, a fork, a bent paper clip), an empty can (aluminum pop can, soup can, etc.) a lighter, your thermometer, and something to hold the can (oven mitt, tongs, pliers, etc.).
1. Get a metal can. Soup cans are mostly steel, pop cans are aluminum. Find its mass. _________g
2. Measure about 100ml of room temperature water. Add it to the can. Find the total mass ________g. Subtract the mass of the can; this gives you the mass of the water ______g.
3. What we have made is a crude calorimeter. Look up the specific heat capactiy of steel or aluminum in colomn 3 of https://en.wikipedia.org/wiki/Table_of_specific_heat_capacities
This device is called a calorimeter. Time for a little math. The heat absorbed by the calorimeter is = (mass of the metal can) x (specific heat capacity of the metal) x (temperature change of the metal) + (mass of the water) x (specific heat capacity of water) x (temperature change of the water).
Oof.
But the metal can is touching the water, so these will be at the same temp. We can pull that out. You can look up both specific heats and multiply them by the appropriate masses, and then get this simplified equation.
(mass metal x sp ht metal + mass water x sp ht water) = calorimeter constant.
The heat gained by the can = calorimeter constant x temperature change.
Back to the procedure.
4. Measure the mass of the snack ______g
5. Figure out how you are going to hold the snack food. If you don’t have tongs, pliers, a fork, etc. … One way is to bend a paper clip into a pyramid. Stick the snack on the clip without breaking it.
6. Whatever you choose, set this all on a very flat paper towel (if the paper towel is up, it might catch fire). A lot of smoke will be produced so you should do this outside, or possibly in your kitchen on the stovetop with your range fan on high if you are in a house and you want to risk the smoke alarm going off. Do not do it indoors in an appartment building where the smoke alarm will set of sprinklers and require evacuation of the building.
7. Make sure that the thermometer is in the water in the can. Hold the can over the snack. Record the starting temperature ____oC. Light your snack on fire and keep the can over the burning snack until the snack goes out AND the water temperature stops going up (it may rise for a little while even after the snack goes out). ____oC Subtract these 2 temperatures to get a temperature change. ___oC.
8. Find the mass of what is left of the snack. _____g
9. Subtract the ending mass from the starting mass. ____g of snack burned up./
10. Use the heat formula from step 3 and the temperature change in step 7 to find the heat the water absorbs. ____J
11. How many joules did the food give off? _____J (hint, this is not a math question, this is a “HAVE YOU BEEN PAYING ATTENTION TO THE PUNCHLINE OF EVERY PREVIOUS PART” question).
12. Convert this to calories (divide by 4.18) = _____ calories, then to (kilo)Calories (divide by 1000) ____ Calories.
13. Divide step 12 by the grams in step 9. This gives you the calories per gram. _____ Calories/gram.
14. Take the Calories per serving size from the package and the grams per serving size from the package and divide these _______ Calories/gram.
15. Compare 14 and 13. How close were they?
16. Usually, they are not very close (13 is usually about half of 14). Why? Look at your paper towel. What is on it. What impact does this have on your calculations? We were trying to measure heat. Where else did the heat go? Were we able to measure this heat? Talk about the sources of error. On the other hand, given this rinky-dink procedure, this isn’t too bad.
17. Calculate your percent error. __________%
