I don't understand q = mc delta T

[nhmllr]

Well, I understand q = mc∆T, along with q = mH_v and q = mH_f

What I don't understand is this graph:
http://dinosaurtheory.com/phase_change.jpg

Well, I mean, I understand THAT graph.

Here's what I don't understand:
Today in chemistry, we received a very similar graph, but the X-axis was labeled "time" instead of "added heat" as it is in the one I linked to.

I raised my hand and pointed out that the independent variable should not be "time" because nowhere in our equations were we even given "time" as a variable! "Time" actually has nothing to do with temperature. I could leave an ice cube on my table and it won't necessarily melt, then vaporize. Or, alternatively, I could throw it into the sun and it would vaporize very quickly. Also, over time I could have water vapor condense into water, then freeze into ice.

The way I see it, "time" has no right to be and independent variable on such a graph.
My chemistry teacher told me that "time" is often an independent variable in graphs, and that energy had to be calculated (meaning that added energy could not be the independent variable if we had to calculate it after the fact). But I could not get over the fact that nowhere in any equation was "time" mentioned, and I couldn't get over that.

My Question: Is time supposed to be the independent variable on this graph? Or is my thought process right in that the X-axis should be labeled "added energy?"

(I understand that time can be the X-axis with the given condition that we're heating something up over time, such that heat = constant x time, but nowhere were we given such a condition.)

 

[jtbell]

If heat is added to the system at a constant rate (calories per second or joules per second), then a graph of temperature versus time looks the same as a graph of temperature versus added heat, except for the horizontal scale.

 

[boneh3ad]

It wouldn't even have to be a constant rate for time to be a valid variable on that axis. It would still need to be constant rate to qualitatively match the graph, of course.

 

[Philip Wood]

heat = constant x time

This equation says it all. Plotting time instead of heat added will give you the same shape of graph. Don't worry about your teacher not mentioning it. You clearly understand what's going on.

 

[PJC01]

I can understand your confusion about the use of "time" as the independent variable on the graph. In thermodynamics, time is not always a relevant factor in understanding the behavior of a system. However, in the context of phase changes, time can be a crucial factor in determining the amount of energy required for a substance to undergo a phase change. This is because phase changes involve a transfer of energy, and the rate at which this energy is added or removed can affect the behavior of the substance.

In the equation q = mc∆T, where q represents heat energy, m represents mass, c represents specific heat capacity, and ∆T represents change in temperature, time may not be explicitly mentioned, but it is still a factor in determining the amount of heat energy required to bring a substance to a certain temperature. This is because the longer a substance is exposed to a certain amount of heat energy, the more its temperature will change.

In the graph you shared, "added heat" is used as the independent variable because it is more directly related to the concept of phase changes. However, in your chemistry class, "time" may have been used as the independent variable to emphasize the importance of time in understanding phase changes.

To answer your question, both "added heat" and "time" can be valid independent variables on a phase change graph, depending on the context and what is being emphasized. It is important to remember that in science, there are often multiple ways to interpret and represent data, and the choice of independent variable may vary depending on the specific situation.

I hope this explanation helps to clarify your confusion. As a scientist, it is important to keep an open mind and be willing to consider different perspectives and interpretations of data. Keep asking questions and seeking understanding, as that is the foundation of scientific inquiry.