Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression...

Evolution shapes the features of organisms over time, ensuring that they are suited for the environments in which they live. Sometimes, selection pressure leads to the rise of similar but unrelated adaptations in organisms with no recent common ancestors, a process known as convergent evolution.

The endosymbiont theory is the most widely accepted theory of eukaryotic evolution; however, its progression is still somewhat debated. According to the nucleus-first hypothesis, the ancestral prokaryote first evolved a membrane to enclose DNA and form the nucleus. Conversely, the mitochondria-first hypothesis suggests that the nucleus was formed after endosymbiosis of mitochondria.
Contrary to the endosymbiont theory, the eukaryote-first hypothesis proposes that the simpler prokaryotic and...

Scientists record evolutionary history by analyzing fossil, morphological, and genetic data. The fossil record documents the history of life on Earth and provides evidence for evolution. However, both fossil and living organisms offer evidence that outlines Earth’s evolutionary history.

One of the distinguishing features of eukaryotic cells is that they contain membrane-bound organelles, such as the nucleus and mitochondria, that carry out specialized functions. Since biological membranes are only selectively permeable to solutes, they help create a compartment with controlled conditions inside an organelle. These microenvironments are tailored to the organelle's specific functions and help isolate them from the surrounding cytosol.
For example, lysosomes in the animal cells...

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.