Consider the following:

•    When two objects with different temperatures are in contact, we see energy flow from the hot object into the cold object.

•    When an exothermic reaction takes place, energy is transferred from the chemical account to the thermal account. After the reaction has taken place, the energy flows from the system to the surroundings.

•    When ice is heated to 0^o C, it begins to melt as energy is transferred to the E_i account.

In each case, how does energy know where to go?

Energy is a conserved, substance like quantity that is causes change. Hot objects have a higher concentration of energy than colder objects. We played a game that models how energy flows between different objects. We learned that though energy flows in both directions, more energy flows from hot to cold than in the other direction. The result is a net transfer of energy from the hotter to the cooler object. 

We can think of the above process as energy diffusion from one place to the other. Both objects have energy, but since the hotter object has more energy than the cooler object, more energy moves from hot to cold than from cold to hot. The system reaches equilibrium when both objects are at the same temperature. Energy continues to move in both directions, but the rate of transfer of energy in each direction is the same.

How is the energy transferred? Particles at the interface collide with adjacent particles transferring some of their energy. A larger difference in the temperature between the two objects will result in a greater rate of transfer of energy. Once the temperatures are the same, the rate of transfer of energy in each direction will be the same.

Energy Transfer

When energy is transferred between two objects with different temperatures, the energy moves in such a way as result in both objects ending up with an equal energy concentration.

•    Two objects, same substance, same amount

The energy has spread out between the two materials. Equal amounts of hot and cold material result in a final temperature half way between the two temperatures.

•    Two objects, same substance, different amounts

 The final temperature is closer to the colder material. The energy has more material in which to spread out.

If we started with 20 g of hot water and 10 g of cold water, would the final temperature be closer to the cold or warm water? Why?

What about two different types of materials at different temperatures in contact?

Specific Heat Capacity

Adding energy increases the speed at which atoms and molecules move or vibrate. This results in an increase in temperature if there is no change in state. If we add a certain amount of energy, Q, to a sample of material, its temperature will increase. If we double the amount of material, the amount of energy needed to raise the temperature by the same amount will double. Specific heat capacity is a measure of the energy required to raise the temperature of 1g of a substance by 1 C. 

Different substances have different specific heat capacities.  The specific heat capacities are different for every element in the Noble gases. As the molar mass increases, the specific heat capacity decreases (i.e. CpXe < CpHe). If we compare their molar heat capacities (energy required to raise the temperature of 1 mole of a substance by 1 C), we see that they are the same. Similar results are obtained for elements in other groups. Per gram, the heat capacities are less for the larger Noble gases because there are a smaller number of these atoms than in the smaller atoms in a 1 g of a sample. For example, 1 g of Xe has fewer atoms than in 1 g of He. Comparing molar heat capacities is more useful because the comparison is based upon the same number of particles.

We see other differences in molar heat capacities of the elements on the periodic table. The diatomic gases have greater molar heat capacities than the Noble gases. Examining the molar heat capacities of compounds also shows differences. Why do the diatomic gases have a greater molar heat capacity than the Noble gases? Why do more complex molecules have larger molar heat capacities than less complex molecules? More complex molecules have more ways energy can be stored. Added energy can be stored in the “spring-like” bonds between the atoms as well as the rotation of the molecule. More complicated molecules have more “springs” that can store more of the added energy. This leaves less energy available to increase the kinetic energy of the molecule. Therefore to achieve a 1 C change in temperature, you’d need to add more energy. These differences in heat capacity can give us insight into the structure of a molecule. A simpler structure results in a lower molar heat capacity whereas a more complex structure results in a larger heat capacity.

A Statistical View of Energy Transfer

How is energy distributed among the atoms in a material? Is it uniformly or non-uniformly distributed? How and why does it move? Up to now we’ve focused on a kinetic explanation, treating energy like particles, that diffuse from one place to another. While energy moves in both directions, there is more movement from hot to cold than cold to hot, so we see a net movement of energy from hot to cold. 

If we examine what happened in the rock-paper-scissors activity, we started out with two populations of people, an inner circle and an outer circle. Initially the outer circle had more energy than the inner circle. Within each circle, each person started out with the same amount of energy.

After playing a number of rounds we see that we ended up with the inner and outer circles having about the same amount of energy, but each person had different amounts of energy. For the same macrostate (same amount of energy in the inner and outer circle), there are a number of possible microstates. The microstates that seemed to be more probable than others were the ones that had several ways of occurring. The system did not return to the initial state. While this microstate was possible, it was not statistically probable because it had only one way of occurring.

             Initial Conditions                          Two of Many Possible                                                                                     Final Outcomes
                 (only one way)                                   (many ways)