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An introduction to heat capacity

This video introduces heat capacity. This is the way that we can measure energy and enthalpy by monitoring temperature changes.
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In the last lecture, we derived a specific form  of energy that chemical reactions can have,   called enthalpy. It’s a convenient  measure of heat given off by a reaction.  Now, usually we think of heat as being  temperature, and hotness… but that’s not entirely   true, because we need to consider  heat capacity. It’s a quantity you may   be already aware of, and it’s something  that appears in lab practicals a lot.  In short, heat capacity is the relationship  between heat, which is an energy, and measured   in Joules, and temperature, which is kind of how  heat and thermal energy manifests in reality,   and is measured in Kelvin. So….
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We label heat transferred “q”.  And for constant pressure, that q  is equal to an enthalpy change.  Enthalpy, as an absolute number, is a specific  measure of energy for a chemical system. This   measure of energy includes its internal energy,  and also the work needed to establish itself,   which is its pressure multiplied by the volume. But, crucially, we can’t measure enthalpy of   a system directly, and we can’t know  the internal energy in absolute terms.  So, instead, we opt to talk only about enthalpy  changes. This is something we can measure,   because it’s that heat given out by a  reaction, that value that we’ve labelled q.  But, how do we measure enthalpy  change? That’s called calorimetry.   And you probably have come across it before.
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The term calorimetry, and calories, and caloric,   come from an out-dated and obsolete theory that  heat was a substance that physically flowed.   Remember, we now know that heat, and the energy  associated with it, is actually a manifestation   of molecular motion. At the sub-microscopic   level, molecules are moving, and banging into  each other, and transferring energy around.  So, the heat that we can measure with a  thermometer is a consequence of all that   molecular-level motion. But, first, let’s   think about direction of heat flow. The thermometer, here, is the “surroundings”.   It’s accepting heat from the system.
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Or you can think of the thermometer as a system,   and its enthalpy is going up because its  absorbing heat from its own surroundings.   Either way, energy is flowing, by these  microscopic interactions, from one place   to another, and this is what we measure. But there is a slight issue with measurements.   Let’s assume we have two flasks. One has  ethanol in it, and another has water.  If we then heat them, with the same heat  source. Maybe that heat is a chemical reaction,   maybe it’s a burner or a hot plate.
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In any case,  the same amount of energy is being transferred.   Over time, we’ll actually see that  they reach different temperatures.  Specifically, the water will heat up more slowly.   Or, at least, the thermometer  will rise more slowly in water.  The same energy is being transferred; it  simply manifests as a different temperature   change. And that’s because both of these  substances have different heat capacities.  Heat capacity is a measure of how much  energy is required to raise the temperature.  The standard units for this is Joules  per Kelvin.
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Or, how many joules of energy   are required to raise the temperature by 1 degree.  That’s one degree Celsius or one Kelvin, remember   the scale is the same, and only  the starting point is different.  But… that’s not the complete  story of heat capacity. The system   has a mass, so we can divide through by mass, and  get something known as the specific heat capacity.  Most of the time, in thermodynamics or any  energy-based discussion, the term “specific”   will refer to “per mass”.  This is the energy required to   raise the temperature of one gram by one degree. We can absolutely make the same argument for   moles, too. And make a molar heat capacity.
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But, most of the time, this is probably   less convenient, because we will be running  reactions in solvents, and it’s easier to   consider solvents in terms of their volume,  and density, therefore mass, than by moles. It’s just a little easier to think of 250  millilitres of water, and therefore 250 grams   of water, than 13.88 moles of water.
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The per  mass measurement can also be for any solution.   Dissolving salts into the water will  change the heat capacity of the solution.   And a per-mass measurement is way more convenient  for dealing with that than a per-mole measurement.   Because 250 grams of water and 20 grams  of salt give us 270 grams of salt water.  A more pressing thermodynamic distinction  is whether this is heat capacity   measured at constant volume, or constant  pressure.
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This is important because it does   change, and it changes whether we’re using units  that will be directly compatible with enthalpy.  So if we want to calculate enthalpy,  which is defined as the heat transferred   at constant pressure, we need C-p, and  multiply it by the temperature change   that we detect with a thermometer, and  the amount, whether it’s mass or moles. 
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One thing to finish off the concept  of heat capacity, is the heat capacity   ratio. I won’t cover the derivation of why this  is the case, here, but this value can be used   to further modify the ideal gas law for adiabatic  conditions, and is useful for accounting for work   done, and is related to the degrees of freedom  within a molecule. This will be all be in the   wider reading, below, if you want to tackle it. And that’s it for heat capacity for now. It’s   a very important concept when trying  to measure energy changes in the lab.

What is heat capacity?

Heat capacity is the way that we can measure energy and enthalpy by monitoring temperature changes.

Enthalpy

Energy is released by reactions – or, sometimes, taken in – in the form of enthalpy. Enthalpy is simply the heat generated, and “heat” manifests as temperature.

Remember: heat is the microscopic motions of molecules, their kinetic and potential energies combined. It’s often very very easy to think about heat as a substance flowing in and out of systems, but this is not the case.

Enthalpy and temperature

The enthalpy released by a reaction manifests as a temperature change. But while these are directly proportional, the proportionality constant is not always the same for each and every substance.

The proportionality constant here is the heat capacity. As an absolute measure, it is usually given in J K-1. I.e. the amount of energy (in J) to raise something’s temperature by 1 K.

This is usually given a specific heat capacity, which is J K-1 g-1.

A more convenient measure of heat capacity

This measure is a significantly more convenient measure of heat capacity than a per-mole measure, simply because masses of substances and mixtures are more easily obtained.

It’s easier to think of 250 g of water (because we can weigh it) than 13.8 moles of water. We can also easily think about 250 g of saltwater, whereas “moles of saltwater” would be less rigorously defined.

Conditions

More important than the amount that we’re referencing heat capacity to is the conditions. Heat capacity at constant volume and constant pressure are two different things. Usually written Cv and Cp respectively.

Note: Subscripts in thermodynamics usually represent the variable that remains constant throughout a change. See the earlier articles about states and paths. This crops up in more advanced material, where the subscripts are added to some differential/calculus notation.

Equations

While I would entirely recommend checking the units of heat capacity in order to see what you do with it, it’s sometimes useful to see it as an equation:

[q=C_p times m times Delta T]

Where q = heat transferred, Cp = heat capacity at constant pressure, m = mass, ΔT = temperature change.

This can be rearranged to predict temperature changes from the energy that has been released.

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Introduction to Thermodynamics

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