Order out of chaos

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

A living cell's primary tasks of obtaining, transforming, and using energy to do work may seem simple. However, the second law of thermodynamics explains why these tasks are harder than they appear. None of the energy transfers in the universe are completely efficient. In every energy transfer, some amount of energy is lost in a form that is unusable. In most cases, this form is heat energy. Thermodynamically, heat energy is defined as the energy transferred from one system to another that is...

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...

Social psychologists have documented that feeling good about ourselves and maintaining positive self-esteem is a powerful motivator of human behavior (Tavris & Aronson, 2008). In the United States, members of the predominant culture typically think very highly of themselves and view themselves as good people who are above average on many desirable traits (Ehrlinger, Gilovich, & Ross, 2005). Often, our behavior, attitudes, and beliefs are affected when we experience a threat to our...

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be put...