Calculating Heat in Calories

[momneedshelp]

Please help me guide my son and his thinking...I am not a math or science person...

 

I hope it's okay if I type the questions and his way of answering it...

 

Cindy made tea. She started with 300g of water at 20C. She transferred 18,000 calories to the water. What was the final temperature of the water.

 

Well, first of all, my answer is....there aren't calories in water! But as I said before I know nothing.

 

My son's work was....multiplying 300 into 18,000, which gave him 54 degrees.

 

Is that right???

 

This is my first thread so if I didn't something wrong...sorry!!!!

 

mom...

[swansont]

There are no calories in digesting water, but calories are a unit of energy, and adding energy will cause a temperature change (we "burn" calories to maintain our body temperature*)

 

1 calorie is the amount of energy it takes to raise the temperature of a gram of water by 1 ºC (assuming no phase change)

 

54 isn't right, since that's from multiplying 18 and 3, ignoring the magnitudes of the numbers, and the units won't work out.

 

[math]\frac{18,000 cal}{300 g} 1 \frac{g ºC}{cal}[/math] gives a temperature increase of 60 ºC, for a final temperature of 80 ºC

 

 

* to add to the confusion, a food Calorie is actually a kilocalorie, and is usually denoted by using a capital "C"

[CaptainPanic]

And while you're at it - tell his teacher that the proper unit for energy is called the "Joule", not the "Calorie".

 

Through a lazy choice of a unit, one physical quantity (namely the "specific heat") is completely overlooked. I think that is very bad education. Leaving out vital information because it is possible will leave the student confused when things become more complicated.

 

The formula you need is:

 

[math]E=m\cdot{C_P\cdot{\Delta{T}}}[/math]

 

with:

[math]E[/math] is the energy (in Joule - For your info, 1 Calorie = 4.184 Joule)

So, 18000 Calories = 75312 J

 

[math]m[/math] = mass, in kg

That's 300 g here, so 0.300 kg.

 

[math]C_P[/math] = specific heat, in J/kgC or J/kgK

That's 4.184*10^3 J/kgK

 

[math]\Delta{T}[/math] in degrees (K or C)

That's the one we want to calculate.

 

changing the formula to calculate the temperature:

[math]\Delta{T}=\frac{E}{m\cdot{C_P}}=\frac{75312}{0.300\cdot{4.184\cdot{10^3}}}=60[/math]

 

The use of Calories is only easy in this very particular case - in all other cases, the use of Joules, and the method I just described is easier and more widely used. Only the USA use calories. The rest of the world uses Joules for energy.

Edited October 20, 2009 by CaptainPanic

[swansont]

Only the USA use calories. The rest of the world uses Joules for energy.

 

Some of us in the US use Joules.

[timo]

Some in the rest of the world use calories .

Energy content of food is regularly given in kcal which -to my amusement- is usually called "calories" (that is: not "kilo-calories").

[John Cuthber]

I will use any unit of energy I like, including the barn yard atmosphere on a bad day.

 

Converting to Joules just so you can divide by the same number again might be good pedantry, but I'm not sure it's helpful here.

 

It's a pity that the Calorie and calorie get abused on food packaging but it's rare that the distinction actually troubles anyone. (Does anyone really think that a bar of chocolate might be only 1/10000 of a day's energy needs, or about enough energy for 100 days?)

People use units that suit their personal experience and the work they are doing. There's not a lot of point trying to stop that so perhaps it's better to teach people how to convert from one unit to another and also to think about the magnitude of the answer and see if it's "just plain silly".

[CaptainPanic]

I will use any unit of energy I like, including the barn yard atmosphere on a bad day.

Good for you. It's not an argument for or against anything, although I hope you'll never design a bridge with such a bad habit.

 

Converting to Joules just so you can divide by the same number again might be good pedantry, but I'm not sure it's helpful here.

I disagree.

Providing a solution to a problem where you choose your quantities such that you give a particular constant the value "1", and then leaving it out altogether because it doesn't affect the outcome is stupid. It means that people will assume that this particular constant doesn't exist. They will not be able to solve any problem that doesn't involve heating water.

 

We are in the "homework" section of the "science forum" aren't we? I'm just asking, so that I am not accidentally posting on the "diet forum for people with a single digit IQ".

 

Apologies to all those who have a single digit IQ and are in need of a diet.

 

It's a pity that the Calorie and calorie get abused on food packaging but it's rare that the distinction actually troubles anyone. (Does anyone really think that a bar of chocolate might be only 1/10000 of a day's energy needs, or about enough energy for 100 days?)

People use units that suit their personal experience and the work they are doing. There's not a lot of point trying to stop that so perhaps it's better to teach people how to convert from one unit to another and also to think about the magnitude of the answer and see if it's "just plain silly".

 

While I agree that not much harm can be done in a miscalculation of the energy of a chocolate bar, actual rockets meant to achieve orbit have fallen from the sky because of conversion errors. If the whole world would just use the SI units, which need no conversion, we wouldn't have this discussion.

 

Calories are not practical, because nobody cares how many degrees they can heat some water after they eat chocolate. The only people who will do such calculations are engineers and scientists, and they should use Joules. So why doesn't the rest of the population follow that brilliant example?

[John Cuthber]

"If the whole world would just use the SI units, which need no conversion, we wouldn't have this discussion."

 

With the information given you would not be able to answer the question in SI units.

You can answer it if you use calories as the unit of energy.

 

Incidentally, are you aware that plenty of us learned how to do this sort of thing using Joules or calories and because of that, could redo the calculations in foot poundals if needs be?

Is this the forum for "people who can only do calculations if they are set out in exactly the right format and units"?

 

Still you will be pleased to know that I won't be designing any bridges any time soon, though the last time I did it (a table really, but the maths is similar) I used SI units.

Sadly, (this was in the days before Google) I only had a list of maximum permissible stresses and Young's moduli in PSI so I had to redo the calculation.

 

I try to leave that sort of thing to civil engineers. BTW, is a civil engineer one who asks politely before building a bridge?

 

Also, do you look forward to the day that McDonalds sell a "hectagrammer" or are you holding out for a Newtonner (with cheese)?

[swansont]

While I agree that not much harm can be done in a miscalculation of the energy of a chocolate bar, actual rockets meant to achieve orbit have fallen from the sky because of conversion errors. If the whole world would just use the SI units, which need no conversion, we wouldn't have this discussion.

 

SI units are not always practical. We physicists regularly use electron-Volts and the aforementioned barn, because they are appropriate to the scale of the problem.

 

In my limited experience, unit conversion helps foster understanding, and it's the engineers (the ones building bridges) that have more problems with needing units to be consistently given, because they don't do the conversions well.

[insane_alien]

in my course at uni, we have to deal with weird units all the time specifically to enable us to deal with whatever comes up. although personally i tend to convert everything to SI and then do whatever mathematical wizardry is required. but only if it's something long and detailed i need to do. if it something like that i'd leave the energy in calories and work it through like that.