Can you calculate entropy

Table This is a generalized plot of entropy versus temperature for a single substance. The entropy change of a reaction where the reactants and products are in their standard state can be determined using the following equation:.

The second law of thermodynamics states that a spontaneous reaction will result in an increase of entropy in the universe. The universe comprises both the system being examined and its surroundings. The change in entropy of the surroundings is essentially just a measure of how much energy is being taken in or given off by the system. We can also calculate a change in entropy using a thermodynamic cycle. As you will discover in more advanced math courses than is required here, it can be shown that this is equal to the following:For a review of natural logarithms, see Essential Skills 6 in Chapter 11 "Liquids".

Thus we can use a combination of heat capacity measurements Equation We can use a thermodynamic cycle to calculate the entropy change when the phase change for a substance such as sulfur cannot be measured directly. Two kinds of experimental measurements are needed:. Because the heat capacity is itself slightly temperature dependent, the most precise determinations of absolute entropies require that the functional dependence of C on T be used in the above integral in place of a constant C.

To this must be added the enthalpies of melting, vaporization, and of any solid-solid phase changes. Furthermore, the system does not affect the entropy of its surroundings, since heat transfer between them does not occur. Thus the reversible process changes neither the total entropy of the system nor the entropy of its surroundings. Sometimes this is stated as follows: Reversible processes do not affect the total entropy of the universe.

Real processes are not reversible, though, and they do change total entropy. We can, however, use hypothetical reversible processes to determine the value of entropy in real, irreversible processes. Example 1 illustrates this point. Spontaneous heat transfer from hot to cold is an irreversible process. See Figure 3. Figure 3. Remember that the total change in entropy of the hot and cold reservoirs will be the same whether a reversible or irreversible process is involved in heat transfer from hot to cold.

So we can calculate the change in entropy of the hot reservoir for a hypothetical reversible process in which J of heat transfer occurs from it; then we do the same for a hypothetical reversible process in which J of heat transfer occurs to the cold reservoir.

This produces the same changes in the hot and cold reservoirs that would occur if the heat transfer were allowed to occur irreversibly between them, and so it also produces the same changes in entropy. First, for the heat transfer from the hot reservoir,. There is an increase in entropy for the system of two heat reservoirs undergoing this irreversible heat transfer.

We will see that this means there is a loss of ability to do work with this transferred energy. Entropy has increased, and energy has become unavailable to do work. It is reasonable that entropy increases for heat transfer from hot to cold.

The decrease in entropy of the hot object is therefore less than the increase in entropy of the cold object, producing an overall increase, just as in the previous example. This result is very general:. There is an increase in entropy for any system undergoing an irreversible process.

With respect to entropy, there are only two possibilities: entropy is constant for a reversible process, and it increases for an irreversible process. There is a fourth version of the second law of thermodynamics stated in terms of entropy :. The total entropy of a system either increases or remains constant in any process; it never decreases. For example, heat transfer cannot occur spontaneously from cold to hot, because entropy would decrease.

Entropy is very different from energy. Entropy is not conserved but increases in all real processes. Reversible processes such as in Carnot engines are the processes in which the most heat transfer to work takes place and are also the ones that keep entropy constant. Thus we are led to make a connection between entropy and the availability of energy to do work. What does a change in entropy mean, and why should we be interested in it?

One reason is that entropy is directly related to the fact that not all heat transfer can be converted into work. Example 2 gives some indication of how an increase in entropy results in less heat transfer into work. Figure 4. The increase in entropy caused by the heat transfer to a colder reservoir results in a smaller work output of J.

There is a permanent loss of J of energy for the purpose of doing work. There is J less work from the same heat transfer in the second process. This result is important. The same heat transfer into two perfect engines produces different work outputs, because the entropy change differs in the two cases. In the second case, entropy is greater and less work is produced. Entropy is associated with the un availability of energy to do work. When entropy increases, a certain amount of energy becomes permanently unavailable to do work.

The energy is not lost, but its character is changed, so that some of it can never be converted to doing work—that is, to an organized force acting through a distance.

For instance, in Example 2, J less work was done after an increase in entropy of 9. In the early, energetic universe, all matter and energy were easily interchangeable and identical in nature. Gravity played a vital role in the young universe. Although it may have seemed disorderly, and therefore, superficially entropic, in fact, there was enormous potential energy available to do work—all the future energy in the universe.

As the universe matured, temperature differences arose, which created more opportunity for work. The temperature in this equation must be measured on the absolute, or Kelvin temperature scale. On this scale, zero is the theoretically lowest possible temperature that any substance can reach. At absolute 0 0 K , all atomic motion ceases and the disorder in a substance is zero.

How are the Kelvin and Celsius temperature scales related?