# Energy required to raise temperature.

1. Jan 8, 2004

### wasteofo2

Is the amount of energy needed to raise the temperature of a substance linear or not? For instance, would it take the same amount of energy to raise a liter of water from 5 to 10 degrees celcius as it would to raise the same volume of water from 80 to 85 degrees celcius?

In fact, I don't even know if temperature is linear or not...

Last edited: Jan 8, 2004
2. Jan 8, 2004

### Bystander

Heat capacities are NOT generally constant.

3. Jan 8, 2004

### LURCH

As I recall from experiments in highschool physics, we heated a container of water over a Bunson Burner (which produces a fairly constant energy output)and the temperature increase was pretty linear, except during phase transitions.

4. Jan 9, 2004

### Staff: Mentor

Specific heat capacity is constant when not dealing with a phase change as Lurch implied.

Temperature is kinetic energy - so to answer your question, I need to know in relation to what? In relation to kinetic energy, yes, of course, its linear. In relation to particle velocity, its parabolic.

Last edited by a moderator: May 1, 2017
5. Jan 9, 2004

### mmwave

As I recall, they are not constant with temperature but are usually specified (at 0 C?) in tables because they don't vary much over temperatures we encounter outside the lab. I'm thinking they vary less than 1% from 0 to 200 C generally.

The second law of thermodynamics demands that Cv does vary over large temperature changes so that it goes to zero as you approach 0 Kelvin.

6. Jan 9, 2004

Yes.

7. Jan 9, 2004

### Bystander

What is this? Hollywood Squares? Everyone posts bulls**t answers off the tops of their heads? The kid asks a question and gets this kind of nonsense? Check your handbooks, gang. Cx[ is NOT, has NEVER been, and NEVER will be a constant for any substance. mmwave is correct in that the variation is of the order of tenths of a percent to a percent over thirty to hundred K ranges, excluding a major temperature dependence from 0 K to what, call it 100 K for this discussion. Further, the change in Cx isn't even monotonic; that is, (dC/dT) can be positive, zero, or negative; technically, one could call C a constant at local maxima or minima, but that's begging the point.

HEAT CAPACITY IS NOT CONSTANT.

8. Jan 9, 2004

### HallsofIvy

Bystander is correct: heat capacity is not a constant, over varying temperatures. It does not, however, change very much for most common substances over most common temperature changes so that temperature change is approximately constant over a small range of temperature change.

It is much the same situation as with "Hooke's Law": the force a stretched spring exerts is not generally a linear function of amount of stretch but any (differentiable) function can be approximated by its linear (tangent) approximation over a small range.

9. Jan 9, 2004

### Staff: Mentor

Easy, Bystander. The point here is one of usage.

Even in undegraduate level chemistry, thermodynamics, and heat transfer classes, its considered/assumed to be constant. For this reason, its much better to call it constant and leave it at that than call it not constant and leave it at that. If you're going to say its not constant, you need to qualify the statement by saying the variability is so small it can be ignored for all but the most extreme cases.

In fact, I've tried to find the actual variation for water from Google and come up empty. Every site I checked just said 1.0cal at stp (by definition). So anyone know what it is at 100C?

10. Jan 9, 2004

### himanshu121

Yes at undergraduate level u can assume it to be constant unless & until A relation of C with T is specified

11. Jan 9, 2004

### Bystander

One thousand one --- one thousand two --- one thousand three --- one thousand four ---

Things gone that far downhill? Uh-uh. People like to remember a constant heat capacity for ideal gases and generalize to everything, but the fact that heat capacity is NOT constant is presented.

This argument is "bass-ackwards;" if you're going to say "constant," it is absolutely necessary to qualify such a statement with "approximately" and "over limited temperature ranges."

You're HVAC, right? Use a handbook! Check Perry! Peek in CRC, even.

Mean? 15 C? 20 C? Or, BTU --- mean? 39F? 60F? Russ, you know better --- I know that you know better --- you didn't graduate without seeing this stuff and demonstrating on an exam that you know it.

Again, see Perry --- you'll find that Cv at 100 is within a couple tenths of a percent of that at 0, and about one percent greater than at 35 (37?).

12. Jan 9, 2004

### krab

I find this a remarkable comment. So I'll remark on it. It reminds me of "gotcha!" type games we played as kids (kid1: How high is Mt. Everest? kid2: 29,035 feet. kid1: Wrong. I heard it got a foot of snow last night.) Some answers while being technically correct are practically irrelevant. Since the question was asked in a non-technical way (he even asked whether temperature is "linear"), I assumed the poster was not interested in 1% variations.

On the 0.001% chance that wasteofo2 needs such details, here they are. Specific heat from 5C to 10C is on average 1.0040 cal/gm/deg.C. Specific heat from 80C to 85C is on average 1.0038 cal/gm/deg.C. So in answer to wasteofo2's question
The answer ala Bystander is NO: It requires 0.0002 times more energy at the lower temperature.

The specific heat is 1.0094 at 0C, goes through a minimum of 0.9982 at 37.5C, and is back up to 1.0074 at 100C.

13. Jan 9, 2004

### Bystander

Well, hell --- I ain't even gonna count to ten this time --- "gotcha" is if I deliberately trick you into falling on your face --- I posted the correct response --- it's up to wo2 to holler for details if he wants 'em --- you butt in with an "incorrection" --- you don't know what you're talking about, don't post.

F'rinstance, density of water is 3-3.5% less at 80-85 C than at 5-10 C, and the mass of one "liter" is then less by 3-3.5% --- OK, you made the same mistake anyone is going to make within this context --- TWICE? That's "GOTCHA." I'll repeat, "Heat capacities are NOT generally constant." Calling heat capacity of water "one calorie per K," without specifying whether it's "mean, defined, 15 C, 20 C," is good enough for govt. work, farm machinery, physicists, and engineers, but IT AIN'T good enough to do decent thermo." And it's a damned fool who assumes that heat capacities of other substances are constant.

14. Jan 10, 2004