Although energy cannot be created or destroyed, the second law of thermodynamics states that when energy is converted from one form to another, some of that energy becomes unavailable for doing work (Figure 8.2B). In other words, no physical process or chemical reaction is 100 percent efficient; some of the released energy is lost to a form associated with disorder. Think of disorder as a kind of randomness that is due to the thermal motion of particles; this energy is of such a low value and so dispersed that it is unusable. Entropy is a measure of the disorder in a system.
It takes energy to impose order on a system. Unless energy is applied to a system, it will be randomly arranged or disordered. The second law applies to all energy transformations, but we will focus here on chemical reactions in living systems.
NOT ALL ENERGY CAN BE USED In any system, the total energy includes the usable energy that can do work and the unusable energy that is lost to disorder:
Total energy = usable energy + unusable energy
In biological systems, the total energy is called enthalpy (H). The usable energy that can do work is called free energy (G). Free energy is what cells require for all the chemical reactions involved in growth, cell division, and maintenance. The unusable energy is represented by entropy (S) multiplied by the absolute temperature (T). Thus we can rewrite the word equation above more precisely as:
H = G + TS (8.1)
Because we are interested in usable energy, we rearrange Equation 8.1:
G = H – TS (8.2)
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Although we cannot measure G, H, or S absolutely, we can determine the change in each at a constant temperature. Such energy changes are measured in calories (cal) or joules (J).1 A change (in energy, or another quantity) is represented by the Greek letter delta (Δ). The change in free energy (ΔG) of any chemical reaction is equal to the difference in free energy between the products and the reactants:
ΔGreaction = Gproducts – Greactants (8.3)
A change in free energy can be either positive or negative; that is, the free energy of the products can be more or less than the free energy of the reactants. If the products have more free energy than the reactants, then there must have been some input of energy into the reaction. (Remember that energy cannot be created, so some energy must have been added from an external source.)
At a constant temperature ΔG is defined in terms of the change in total energy (ΔH) and the change in entropy (ΔS):
ΔG = ΔH – TΔS (8.4)
Equation 8.4 tells us whether free energy is released or required by a chemical reaction:
If ΔG is negative (ΔG < 0), free energy is released.
If ΔG is positive (ΔG > 0), free energy is required.
If the necessary free energy is not available, the reaction does not occur. The sign and magnitude of ΔG depend on the two factors on the right side of the equation:
ΔH: In a chemical reaction, ΔH is the total amount of energy added to the system (ΔH > 0) or released (ΔH < 0).
ΔS: Depending on the sign and magnitude of ΔS, the entire term, TΔS, may be negative or positive, large or small. In other words, in living systems at a constant temperature (no change in T), the magnitude and sign of ΔG can depend a lot on changes in entropy.
If a chemical reaction increases entropy, its products are more disordered or random than its reactants. If there are more products than reactants, as in the hydrolysis of a protein to its amino acids, the products have considerable freedom to move around. The disorder in a solution of amino acids will be large compared with that in the protein, in which peptide bonds and other forces prevent free movement. So in hydrolysis, the change in entropy (ΔS) will be positive. Conversely, if there are fewer products and they are more restrained in their movements than the reactants (as for amino acids being joined in a protein), ΔS will be negative.
DISORDER TENDS TO INCREASE The second law of thermodynamics also predicts that as a result of transformations involving energy, disorder tends to increase; some energy is always lost to random thermal motion (entropy). Chemical changes, physical changes, and biological processes all tend to increase entropy (see Figure 8.2B), and this explains why some reactions proceed in one direction rather than another.
How does the second law apply to organisms? Consider the human body, with its highly organized tissues and organs composed of large, complex molecules. You might think that this order and complexity are in conflict with the second law—
Getting ordered is coupled to the generation of disorder. Making 1 kg of a human body (soft tissues, not bones) requires the catabolism of about 10 kg of highly ordered biological materials (our food), which are converted into CO2, H2O, and other simple molecules. So this process creates far more disorder (more energy is lost to entropy in the small molecules) than the amount of order (total energy; enthalpy) stored in large molecules in 1 kg of a person.
Life requires a constant input of energy to maintain order. Without this energy, the complex structures of living systems would break down. Because energy is used to generate and maintain order, there is no conflict with the second law of thermodynamics.
Having seen that the laws of thermodynamics apply to organisms, let’s see how these laws apply to biochemical reactions inside the cell.
1A calorie is the amount of heat energy needed to raise the temperature of 1 gram of pure water from 14.5°C to 15.5°C. In the SI system, energy is measured in joules. 1 J = 0.239 cal; conversely, 1 cal = 4.184 J. Thus, for example, 486 cal = 2,033 J, or 2.033 kJ. Although they are defined here in terms of heat, the calorie and the joule are measures of mechanical, electrical, or chemical energy. When you compare data on energy, always compare joules with joules and calories with calories.