Sign conventions in Thermodynamics:
The heat, which we called q, is defined as the heat absorbed by our system. Heat, q, as a "signed algebraic quantity," which means that it can be positive or negative.
That is if q > 0 we say that the object gained heat - heat flowed into our sample, the system absorbed heat. Likewise if q < 0 we say that our object lost heat, heat flowed out of our sample, the system lost heat.
The temperature change, DT,
is also a signed quantity. It can be positive or negative. It is obvious
that if DT > 0 then the temperature increased
and if D T < 0 then the temperature decreased.
Clearly whenever DT > 0 then q
> 0, and vice versa.
Changes of State
If you have a glass of ice water (the glass contains both ice and liquid water) and you add some heat to the ice water the temperature does not change. The heat melts some the ice rather than changing the temperature of the system.
The conversion of ice to water (at 0 oC) is called a "phase change."
Likewise, if you added some heat to a beaker of water at 100 oC (the normal boiling point of water) the temperature of the water would not increase. You would just vaporize some of the water. The conversion of liquid water to water vapor is another phase change.
There is no increase or decrease in temperature when heat is added or withdrawn at a phase change.
There are several different types of phase changes.
solid ® liquid is called melting or fusion (¬ is freezing)
liquid ® gas (vapor) is called vaporization (¬ is condensation)
solid ® gas (vapor) is called sublimation
solid A ® solid B
Examples of solid ® solid phase changes are
S(monoclinic) ® S(rhombic)
Sn(white) ® Sn(gray) (13oC)
C(diamond) ® C(graphite)
Phase changes require energy (in the form of heat), but you already knew that. You have to add heat to melt ice or to vaporize water.
Once again, the amount of heat required to make a phase change depends on the material and the amount of material.
There are tables of heats of fusion (sometimes called latent heat of fusion) and heats of vaporization (or latent heat of vaporization).
The heats of phase changes are usually listed in the tables in J/mol, although you can calculate the value in J/g by dividing by the formula weight.
Examples of some heats of phase changes are:
MP fusion BP vaporization
Ag 1234 K 11.3 kJ/mol 2436 K 250.6 kJ/mol
H2 13.96 K 0.117 kJ/mol 20.38 K 0.916 kJ/mol
H2O 273.15 K 6.008 kJ/mol 373.15 K 40.656 kJ/mol
How much heat does it take to vaporize 1.000 L of water at 100oC?
First, calculate the number of grams of water in 1.000 L of water.
Calculate the number of moles of water in that many grams.
Multiply the number of moles times the molar heat of vaporization of water at 100oC.
How much heat is liberated when 1.00 g of liquid water freezes at 0oC?
Find the number of moles of water in 1.00 g.
Multiply by the molar heat of fusion of water at 0oC.
Thermodynamics simplifies things by dividing the universe up into two parts.
The system is the sample, or object, or apparatus we are interested in.
We usually care about the details of the our system.
The surroundings is everything else.
We usually do not care about the details of the surroundings.
Thermodynamically speaking, then we say that
System + Surroundings = Universe
We saw that the First Law of Thermodynamics said that energy in conserved. In order to put this in the form of an equation we need to give a symbol for energy.
Define the Internal Energy, E, of a system as the sum the kinetic and potential energies of all the particles in the system. (We will not ever calculate a value of E, but we may be interested in the change in E, which we will call DE, as the system undergoes some process or change.
As we have seen before:
DE = Efinal - Einitial.
Clearly, if q > 0 then E is increased and vice versa.
However, adding or removing heat is not the only way to change the internal energy. We can change the internal energy of our system by doing work on the system or by allowing the system to do work on the surroundings.
Define work, w, as work done on the system. That is, w > 0 when we do work on the system and w < 0 when the system does work on the surroundings. In the first case the internal energy of the system increases, in the latter case it decreases.
We now have the equipment to write the first law of thermodynamics in the form of an equation:
DE = q + w.
It is clear that the internal energy of our system goes up or down depending on how much heat is transferred in or out of the system and how much work is done on the system or done by the system on the surroundings.
One of the ways that we can do work on the system is to compress it. Or, if the system expands against some kind of pressure, the system will do work on the surroundings.
(Another form of work is electrical work, but you will not deal with electrical work until next semester when you learn about electrochemistry.)
Again, most of the time we are working in a laboratory open to atmospheric pressure. So our expansion work comes from our system (sample) expanding against the atmospheric pressure or contracting under the atmospheric pressure.
For example, when we cool a sample open to the atmosphere the sample contracts. in this contraction the atmosphere pushes on the sample so that we have done work on the system.
Call the work done on the system in an expansion or a contraction process, wexp. If the sample contracts wexp > 0; if the sample expands, then, wexp < 0.
If we do not have electrical work, or any other work other than expansion and contraction, then the first law can be rewritten as:
DE = q + wexp.
Our most common experience is that our experiments are done on a laboratory bench open to atmospheric pressure. In this case the pressure, p, on the system is constant. Using a subscript, p, to indicate that pressure is being held constant, we can rewrite the first law as,
DEp = qp + wexp.
In the laboratory we usually measure the heat absorbed by or released from our system. In this case the wexp seems to get in the way.
Accordingly we define a new quantity, which has units of Joules, H, called the enthalpy. Enthalpy was referred to as the "heat content" in the early days of thermodynamics, but that name is no longer used. Enthalpy is defined such that,
DHp = DEp - wexp.
From this definition we see that
DHp = qp.
(It is necessary that pressure be held constant for this relationship to be true. I pressure is not constant this relationship does not hold. You can still define enthalpy and DH, but the relationships of these quantities to E and DE is more complicated.)
All of the phase changes we discussed above take place at constant pressure. Thus the heats involved are heats at constant pressure. That is, they can be called qp.
It is customary to use DH rather than q for situations like these. The various heats involved in the phase changes are called DHfus, DHvap, DHsub, and so on. It is understood that in these cases the pressure is held constant.
Let's do one more example of a phase change using the correct language.
What is the enthalpy change in melting 500. g of Ag at 1234 K? From the tables we find that DHfus = 11.3 kJ/mol for Ag at 1224 K (which is the normal melting point of silver).
Moles Ag = 500. g/(107.9 g/mol)
DH = 11.3 kJ/mol ´
Heats of Chemical Reactions
Chemical reactions almost always give off heat or absorb heat. In this course we will refer to the heat of reaction as DH. Before we discuss heats of reaction we need to be more specific about how we are going to discuss chemical reactions.
We said that a chemical reaction always has the form,
reactants ® products.
DH = Hproducts - Hreactants,
even though we will never look at an individual H for any substance.
Here's what we didn't tell you. The chemical reactions we will do calculations on always have the form
reactants(isolated, pure, at temperature, T, and pressure, p)
products(isolated, pure, at temperature, T, and pressure, p).
The temperature, T, is usually 25oC and the pressure, p, is usually 1 atmosphere.
Example, consider the reaction
2 HCl(g) + Na2CO3(s) ® 2 NaCl(s) + CO2(g) + H2O(l).
This reaction will get hot. How do we deal with that?