Figure 1. Parts of a heat exchange graph.
In Physics I, we discussed energy. If we consider a car, a mechanism to change
the kinetic energy of the car is to do work on the car, a macroscopic force
acting through a distance.
In addition to externally observed energy like overall kinetic energy, an object
can have “Internal Energy”, U, which depends on the
phase of the material (solid, liquid, gas), temperature, and possible some other
factors like volume.
We can change the internal energy of an object or system by two mechanisms,
work, W, and heat, Q. With heat, we transfer energy by a different mechanism,
one that typically involves microscopic events. Conservation of energy for systems
involving work and heat is called the First Law of Thermodynamics.
delta U = Q –
W
where Q is energy added by the heat mechanism, and W is work done by the system,
hence reducing the energy.
Calorimetry refers to changes in temperature or changes in phase where no noticeable work is being done. Hence delta U = Q. The calorimeters we will discuss will be closed isolated systems with no change in energy, so that the net heat Q = 0. In chemistry, calorimetry with chemical reactions is important. We will avoid chemical reactions in this class.
1. A sample of mass m staying in the same phase, but changing temperature
by delta T:
Q = m c delta
T Eq 1
The symbol c is a property of the material called the specific heat. Experimental
measurements of the specific heat show that it has a very small change over
wide ranges of temperature (several hundred °C), so we approximate the data
with a Taylor series and keep just the constant term. Values are tabulated in
the text and in various references.
2. A sample of mass m changing phase (melting, etc.) where the temperature
remains constant:
Q = ±
m L Eq
2
L is the latent heat of transformation for the material and is tabulated. Chemists
refer to this with the symbol delta H, the change in enthalpy.
The direction of the phase change just changes the sign, thus for melting Q
= + m L, while for freezing Q = - m L. For this transition L is called the Latent
Heat of Fusion. For boiling or condensation L is called the Latent Heat of Vaporization.
In calorimetry we are seeing the transfer of energy from one material to another
until equilibrium and a single final temperature is reached.
A very helpful way to keep track of calorimetry is with what I will call a temperature-time graph. Suppose that heat is added (or removed) at a constant rate. The graphs below show the effect of no phase change but a temperature change (left two graphs) and a phase change with no temperature change. These are just meant to be quick sketches, don’t sweat the details. Each line segment must have an equation with it, either Eq 1 or Eq 2. constant temperature.
Figure 1. Parts of a heat exchange graph. |
 Figure 2 Two examples of a complete heat exchange graph, mixing cream and coffee, and adding an ice cube to coffee. |
In the following examples you may ignore the effect of the material of the
calorimeter can. In real life you would need to include terms from Eq 1 for
the can itself.
Problems to try:
1. I add 150.0 grams of copper at an initial temperature of 90.0°C
to a calorimeter with 50.0 g of water at 10.0°C. Find the final temperature
of the mixture.
2. I add 9.0 g of ice at an initial temperature of –15.0°C to
a calorimeter with 40.0 g of water at an initial temperature of 35.0°C.
Find the final temperature.
3. I add 18.0 g of ice at an initial temperature of –15.0°C
to a calorimeter with 40.0 g of water at an initial temperature of 35.0°C.
Find the final temperature.
This page maintained by Anne G. Young. Last modified 13-May-2005 .