Now let's worry about how we actually measure energy changes. We might be interested in how much heat (q) is gained or lost from our system, or we might want to know ΔU or ΔH for a reaction or phase change. In any case, we do not have an energy meter and so cannot measure this value directly. This is why we seldom see absolute values of U or H, and why we had to establish the concept of enthalpy of formation for tabulating thermodynamic data. In thermodynamics we deal with changes in energy.

The most common way to follow energy changes is by measuring one or more of the state variables: T, V or P. If our measurement holds one of the state variables constant, say volume or pressure, and all that is occurring in our system is that it is gaining or losing heat, we have a relatively straightforward temperature measurement to make:

at constant volume ΔU = q_V = C_V ΔT

at constant pressure ΔH = q_P = C_P ΔT

We simply measure the temperature of the system at the beginning and at the end of the change in state. These equations assume that 1) we know the heat capacity for the system of interest and 2) the heat capacity remains constant throughout the energy change.

The problem is that, while good for simple calculations involving heat flow, these are not good assumptions for most chemical reactions or phase changes. But suppose we carry out our reaction in thermal contact with something of known heat capacity whose purpose is only to take in or give off the heat evolved or consumed by our chemical reaction? Water is generally used for this purpose and if we carry out our reaction (the system) in thermal contact with the water

q_system = - q_water= - C_water ΔT_water

and we can measure the heat change in the system by measuring the temperature change in water. This type of measurement is called calorimetry. Note that here, as in other parts of this thermodynamics module, ΔT is the final temperature minus the initial temperature.

A very simple constant-pressure calorimeter that can be used to measure q_p (and thus ΔH) can be constructed from a styrofoam cup and is therefore called the coffee cup calorimeter (See movies of a coffee cup calorimeter). The specific heat of water is 4.187 Joules/g-K and if we assume the density of water remains constant at 1g/ml over the temperature range of interest, we can estimate the heat of the reaction as

q_system = - (4.187 J/K) V_water ΔT_water

where V_water is the volume of water used in milliliters. Since the coffee cup calorimeter is used at constant pressure, q_system = Δ_rH for the specific amount of reactants used and all that remains is converting this extrinsic value to one of molar quantities.

If we are, instead, interested in Δ_rU and constant volume measurements, we can perform the reaction inside a closed metal container, which will have constant volume, and perform the calorimetry by immersing the metal container (called a bomb!!) in a known quantity of water. Bomb calorimeters are used in industry and in upper level college laboratory courses.

In practice, bomb calorimetry is much more accurate than is coffee cup calorimetry, but the bomb, itself, has a heat capacity that has to be calibrated. This is done by burning a specific amount of a compound with a know heat of combustion and measuring the change in temperature. The calorimeter heat capacity, which includes the water, can then be determined by working backwards

C_bomb = - ΔT/q_reaction

Once you have calibrated the calorimeter heat capacity, you can then use it to measure the heat for the reaction for which Δ_rU is to be determined.

Note that the "Δ" and the subscripts on the enthalpy are missing from the Δ_rH^o terms in this web page. The subscripts are often omitted because you can get the kind of enthalpy (enthalpy of reaction, solution, vaporization, etc.) from the context and superscript "o" is often substituted for "o" or omitted altogether, again because you can get it from context. However, the "Δ" is not optional and never should be omitted. The "heats" or enthalpies of reaction are changes in enthalpy and not absolute energy values.

An animated dry-lab calorimeter experiment for measuring heats of reactions can be accessed by clicking here. Constant pressure calorimetry can be a good, simple experiment for high school students, as for example the heat transfer AP chemistry lab involving a coffee cup calorimeter. This latter site includes a pre-lab exercise.