Maybe this is more than the OP bargained for, but here are my thoughts:
There are other members with greater understanding of physical chemistry than I have, but perhaps we can make a start. Temperature is an intensive property, whereas heat is an extensive property. Extensive properties depend on the size of the sample, but intensive ones do not.
Babcock_Hall's thought is an excellent place to start. However, I think calling heat an extensive property can be misleading, even if it's not incorrect.
To the OP: Let's start with temperature. What is it? Perhaps we can begin by looking at how we measure it. Let's consider a thermometer. It's not like a ruler, which measures a physical dimension of an object, or a scale, which measures an intuitive physical property like weight. [Although, that's a fun thing to dig into too if you really want to twist your brain.] Of course, like weight we have an intuitive feel for what temperature is and how a thermometer responds if it changes. 'Hot' and 'cold' have a real and relevant - if subjective - meaning to our daily lives, after all. If you take a thermometer sitting on your kitchen counter and stick it in the freezer, anybody can predict correctly that the reading on the bulb will drop, and rather quickly, but why does it do so?
Temperature is a rather abstract concept. And as an abstract concept there are lots of ways to define it. One way which gets at the topical question is this:
the temperature of a system is a relative measure of the average kinetic energy of all the particles in a macroscopic system. Notice an important point here: the temperature does not simply
equal the amount of kinetic energy of all the particles in the system. It is
proportional to the average kinetic energy of all the particles in the system.* That's a vital distinction to understand. Temperature is (1) a relative quantity rather than absolute one (like potential energy) and (2) has a deeply embedded statistical meaning. By the latter point I mean that temperature is only relevant to macroscopic systems consisting on many particles, because it is representative of an average kinetic energy of a multitude of microscopic entities. It really makes no sense to speak of the temperature of a single electron, or a single molecule. Rather we speak of the temperature of a glass of water (gazillions of water molecules) or the air outside on a winter night (gazillions of air molecules). There will always be a range of molecular speeds at a given time, but the statistics are reasonably predictable, so we can define a property which relates to their statistical average.
Point (1) deserves some elaboration as well. You might ask why we use temperature, a quantity that's proportional to average kinetic energy, rather than just using an absolute kinetic energy directly. Why complicate our lives so? The reason is because, at least as far as chemistry and other dynamic sciences are concerned, we're not so much interested in how much absolute kinetic energy a system has, but rather how much kinetic energy the system has compared to how much another neighboring system has (or the same system at different times). When you say, 'It's hot outside today!', the important point you're trying to convey isn't that the atmospheric gas molecules have so-many-kilojoules of kinetic energy today! It's that it feels hot compared to something else: the temperature yesterday, the temperature inside your air-conditioned living room, or - although you may not often think of it this way - the temperature on the surface of your skin. We use temperature rather than an absolute measure of kinetic energy because the absolute kinetic energy doesn't mean much. It's the difference in kinetic energy between systems that drives changes in chemistry, or weather patterns, or human behavioral patterns. This is because when you speak of the amount of kinetic energy a system has, it's related to the capacity of the system to do work (or have work done on it). In that sense, it's much easier to measure something proportional to average kinetic energy than average kinetic energy itself, because we just have to have a convenient and easily measured reference point and scale everything else accordingly. Hence a proportional quantity like temperature. The constant of proportionality here, by the way, is the Boltzmann constant on a per molecule basis or the gas constant R on a per mole basis, adjusted by the number of classical degrees of freedom of the system.
Anyway, this brings us back to the thermometer. I suppose if you had some sophisticated instrument, you could take kinetic energy measurements of gas molecules in your kitchen, then take similar measurements in your freezer, and come up with some relative kinetic energy quantity to describe the absolute difference in (average) molecular kinetic energy between the two systems. But this would be cumbersome and to make such results meaningful when comparing to other freezers, you'd have to normalize them for the amount of space in the system, the relative humidity, and so forth. It'd be a mess. What you need is a proxy that preserves the information you care about without getting into all the details. It is much easier to just take a thermometer from your kitchen, where the average kinetic energy of gas molecules is relatively high, and place it in your freezer, where the average kinetic energy is relatively low, and measure the relative difference by observing how some property of the molecules in the thermometer change.
We know that the density of ethanol, or any liquid, changes as a function of temperature, which translates into a change in volume because the mass is fixed. So when it gets cold, the volume of the ethanol decreases. To quantify this degree of decrease, we use a temperature scale. At a microscopic level what is happening is that on the kitchen countertop, the ethanol molecules are in thermal equilibrium with the atmosphere in the kitchen, bouncing around and vibrating and rotating with some overall average kinetic energy. When we place the thermometer in the freezer, the ethanole molecules initially have a substantially larger amount of average kinetic energy than the surrounding atmosphere. But collisions of ethanol molecules with the glass walls of the thermometer are inelastic, which means that every collision results in some transfer of kinetic energy to the molecules in the glass, and then eventually to the air molecules in the freezer. Because the freezer is much larger than the thermometer, it can be considered as a practically infinite heat reservoir, and thus slowly the average kinetic energy in the ethanol will drop until it approaches that of the external system. All the while, the volume of the ethanol is changing, because as kinetic energy is lost, molecules are moving less quickly, and the total space occupied shrinks. We measure this difference in volume and correlate it to the negative change in mean kinetic energy of the ethanol molecules - which at equilibrium is equal to the mean kinetic energy of the external environment. The change in volume is thus proportional to the change in average kinetic energy (more or less). Of course, in the real world, when someone asks, "How cold is your freezer?", nobody answers "It's 500 microliters of ethanol different than my kitchen counter!" I suppose you COULD use this as your scale if you wanted to, but for various reasons it isn't practical to do so. Instead we use a standardized temperature scale, the reference point of which is either the freezing point of water (in the Celcius scale), or, for Kelvin, the point at which there is no (classical) kinetic energy at all - absolute zero. Even in this latter case, the scale itself (the numerical value) is still related arbitrarily to the properties of water. Nobody thinks about how what they're actually measuring is average kinetic energy because we're so accustomed to dealing with temperatures instead, but that's effectively what we're doing.
Now, it might make sense to inquire: why do we care about all this kinetic energy stuff anyway? I've already stated that the absolute (average - implied from here on out) kinetic energy isn't imporant to know in most cases. Rather, it's the differences in kinetic energy between systems that chemists care about. Why? Because it is differences in energy that drive chemical and physical changes. When you know what the temperatures of two systems are when you bring them into contact, you can predict what is going to happen: one will increase in temperature and the other will decrease, until they meet somewhere in the middle. (You could get this same prediction from using absolute measurements of kinetic energy, but I hope I've established why temperature is a much simpler way to go about it.) Now, if you're astute, you're probably already ahead of me here, but the next question is: yes, we know the temperature of the two objects will be equal when they reach equilibrium, but what will be the equilibrium point? If I drop a heated penny into a bathtub of water, surely the final temperature will be different than if I drop it into a shot glass. Likewise, if I drop a heated penny into a glass of water versus a glass of vegetable oil, do I expect the final temperature to be the same or different once equilibrium has been reached? And do I expect that equilibrium will take the same amount of TIME to be reached in each case?
Enter the concept of heat.
I've mentioned earlier that temperature is proportional to the average amount of kinetic energy of all the particles in a system. But the thing is that the constant of proportionality differs from substance to substance. The reason is because different substances have different ways that kinetic energy can be distributed. Particles in an ideal monatomic gas, for instance, are pretty much restricted to linear translational motions in three dimensions. In this case, the (classical!) average kinetic energy per particle is given by the simple equation (3/2)kT, where k is the Boltzmann constant. The same result can be derived from statistical mechanics. In an real, polyatomic gas - or a liquid or solid - the molecules themselves are moving about, but individual atoms in each molecule are also moving independently in an independent frame. We know these additional degrees of freedom as vibrations and rotations. These motions also contribute to the overall kinetic energy, which changes the constant of proportionality between the average kinetic energy and the temperature. The way this constant of proportionality changes as a function of degrees of freedom for a system is embodied in the heat capacity.
So then what is heat? I like to think of heat as an energy currency that quantifies how the average kinetic energy of a system will change when it's brought into contact with another system at another system. I opened this post by stating that calling heat an extensive property can be misleading, and that's because it's not really a property of an isolated system. You don't usually say, "This cup of water has so-many-Joules of heat in it."** What you would say is, "This cub of water lost so-many-Joules of heat when I placed it in the refrigerator." Alternatively, you would say the freezer gained so-many-Joules of heat. That is, heat is not a property of an isolated system so much as it is a description of the energy exchange that happens when two systems are brought into contact with each other, creating a non-equilibrium situation. The very word 'thermodynamics' means motion of heat. Heat is not a static property. It's a currency that describes a kinectic process. Heat is pumped out of the house by your air-conditioner; it is brought into the house by your furnace. Heat naturally flows from a region of high potential energy and high kinetic energy into a region of low potential energy and low kinetic energy. To go in the opposite direction requires work. At a microscopic level, the transfer of heat means taking some of the average kinetic energy of particles in one part of a system and transferring it to particles in another part of the system (either passively, if it's thermodynamically spontaneous, or actively, if you are using work). The amount of heat is the amount of energy transferred. By using the amount of heat along with the heat capacity - a fundamental property of the system - you can determine how the temperature has been changed, which again is proportional to the overall amount of kinetic energy in the system.
So: if you drop a hot penny into a cup of water, the hot penny will cool and the water will heat until they have the same equilibrated temperature. This happens because kinetic energy leaves the penny and enters the water until equilibrium has been reached: the net kinetic energy transfer is the same in both directions. On a per-particle basis, though, the copper atoms in a penny can store a different amount of kinetic energy than the water molecules in water, and the amount of each substance will be different, so the final temperature will not likely be an average of the two starting temperatures. The transferred heat is the total amount of kinetic energy that is transferred from the penny into the water. That's the currency that is used to raise the temperature of the water, adjusted by the heat capacity - the macroscale constant of proportionality between the temperature and the average kinetic energy per molecule or mole of water. If I put the same penny in some other substance, the same amount of heat may be transferred, but the final temperature will be different. This is because that transferred heat gets partitioned into the various degrees of freedom of the medium into which it's being transferred. In a substance with a high specific heat, there are lots of ways that heat can be distributed, so that heat raises the average kinetic energy per particle by only a small amount, and the temperature only increases slightly. In a substance with a low specific heat, there are only a few ways that heat can be distributed, so that quantity of heat raises the average kinetic energy per particle by quite a bit, and the temperature increases proportionally.
To sum, then: Heat is basically the absolute amount of kinetic energy transferred when two macroscopic systems with different average kinetic energy per particle are brought into contact with each other. Temperature is a representation of how much kinetic energy there is in a system per particle, scaled by the number of ways that the kinetic energy can be distributed among the various particles and their allowed motions.
Well, I suppose I could keep going, relating heat to enthalpy and so forth, but I think I'll stop there. Maybe you found some of that useful. Maybe not.
* A brief footnote: kinetic energy is not the only thing temperature is proportional too. A more thermodynamical or statistical mechanical perspective would say that temperature is the proportionality constant between internal energy and entropy. In the end, though, the concept is the same - temperature isn't something physical that's being measured directly. It's a placeholder representing something else fundamental about the system. In both definitions (kinetic theory vs. thermodynamic), there's also a statistical interpretation underneath it all. While the thermodynamic and kinetic theory viewpoints approach the question from different directions, ultimately they are equilivalent solutions to the problem.
** Although you could say this if you wanted, IF you bared in mind that you still have to compare it to some frame of reference. The natural one would be the cup of water at absolute zero, which would be the point where the average classical kinetic energy is equal to zero. This would be the theoretical maximum amount of heat the cup of water could lose if it were put into an infinite reservoir held at absolute zero temperature. But that's a rather abstract extrapolation so I still maintain that saying "This cup was so-many-Joules of heat in it," isn't practically meaningful. For the same reason, even though we could say that a cup of water has some amount of enthalpy in it, when using thermodynamic terms like this we almost always see them in the context of change. It is the CHANGE in enthalpy that we are interested in, not some absolute value. Just so with heat.
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Topic: I can't grasp the difference between temperature and thermal energy.. (Read 2878 times)