What is the difference between a mixture and a compound?

According to most textbooks:
  • a compound is an entity consisting of two or more atoms, commonly from different chemical elements, which associate via chemical bonds.
  • On the other hand, a mixture is a material made up of two or more different substances which are mixed but are not combined chemically.
So the difference is that a mixture refers a physical combination of substances, whereas a compound refers to a chemical combination.


But these definitions do not say anything unless we establish the difference between a chemical and a physical combination and, according to the same textbooks:
  • a chemical process is a method or means of somehow changing one or more compounds,
  • whereas physical changes are changes affecting a substance, but not its chemical composition, because they do not change chemical bonding.
As you probably have already realized, the definitions are circular! We put two substances together. If the process is not chemical, what we obtain is a mixture, not a compound. But we defined a non-chemical process as the one where the compounds are still the same compounds, but mixed. Who is Alice? She is Bob's cousin. And who is Bob? Alice's cousin. We still do not know who is Alice!

Are you able to give a definition of compounds and mixtures that is not circular? How can we define chemical process without saying that a chemical process is different from a physical one in that compounds change?

Notice the distinction cannot come from the physical properties if the substance, because the physical properties of a mixture may differ from those of the components. In addition, evolved or absorbed heat cannot be the solution because, both in chemical reactions and in mixtures, heat is either evolved (an exothermic process) or absorbed (an endothermic process).

Please, explain your reasoning. You can post your attempted answers in the comment box below. Please, do not use Facebook or Twitter to give your answers. 

Why don't protons in a nucleus repel each other?

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom.
A model of the atomic nucleus showing it as a compact bundle of the two types of nucleons:
protons (red) and neutrons (blue).
By Marekich - Own work (vector version of PNG image), CC BY-SA 3.0, Link

The atomic number Z of a chemical element is the number of protons found in the nucleus of an atom. Since neutrons are neutral while protons are positively charged with a charge that is, in absolute value, equal to the electron charge, the atomic number is identical to the charge number of the nucleus. In an uncharged atom, the atomic number is also equal to the number of electrons, and that is why the atomic number uniquely identifies a chemical element. For instance, Z=1 is called hydrogen and Z=6 carbon.

The world nuclide is referred to a 'species of nucleus', characterized by its number of protons Z, its number of neutrons N, and its nuclear energy state. Identical nuclei belong to one nuclide, for example each nucleus of the carbon-13 nuclide is composed of 6 protons and 7 neutrons. On the other hand, the members of the group of all the nuclides of the same elements are called isotopes. That is, the nuclides with equal atomic number, i.e., of the same chemical element but different neutron numbers, are called isotopes of that element.

Stable nuclides are nuclides that are not radioactive and so (unlike radionuclides) do not spontaneously undergo radioactive decay. It has been found that there are 80 elements with one or more stable isotope. For instance, carbon has 15 known isotopes, from carbon-8 to carbon-22, of which carbon-12 and carbon-13 are stable.

But, because of the fact all the protons have the same charge and are very closed to one another in the nucleus, one expects that they repel each other by a strong electric force, a force that must be much stronger than the force acting between the nucleus and the surrounding electrons. This force should make the nucleus explode. Therefore, no nuclide with more than one proton should be stable, that is, the only stable element should be hydrogen!

Please, explain your reasoning. You can post your attempted answers in the comment box below. Please, do not use Facebook or Twitter to give your answers. 

Why do astronauts float weightless in the International Space Station?

A rearward view of the International Space Station backdropped by the limb of the Earth. In view are the station's four large, gold-coloured solar array wings, two on either side of the station, mounted to a central truss structure. Further along the truss are six large, white radiators, three next to each pair of arrays. In between the solar arrays and radiators is a cluster of pressurised modules arranged in an elongated T shape, also attached to the truss. A set of blue solar arrays are mounted to the module at the aft end of the cluster.

We have seen on TV that astronauts float weightless in the International Space Station (ISS), and during spacewalks. In fact, the ISS serves as a microgravity research laboratory in which crew members conduct experiments in biology, physics and other fields. Microgravity is more or less a synonym of weightlessness and zero-g (zero gravitational field strength).
Nevertheless, the ISS maintains an orbit with an altitude h of between 330 and 435 km so, according to Newton's law of universal gravitation, the gravitational field strength g in the ISS is:
where G is Newton's constant, M mass of Earth and R is the radius of Earth.

Taking into account that the gravitational field strength at the surface of the Earth is g=9.8 m/s^2, we conclude that things and astronauts inside the ISS weigh only a 10% less than they do on Earth! The weight is almost the same! How is this possible?

Please, explain your reasoning. You can post your attempted answers in the comment box below. Please, do not use Facebook or Twitter to give your answers.

Preparation for the International Physics Olympiad (IPhO): Electromagnetism

The IPhO syllabus includes:

2.3 Electromagnetic fields
  • 2.3.1 Basic concepts: Concepts of charge and current; charge conservation and Kirchhoff's current law. Coulomb force; electrostatic field as a potential field; Kirchhoff's voltage law. Mag­netic B-field; Lorentz force; Ampere's force; Biot-Savart law and B-field on the axis of a circular current loop and for simple symmetric systems like straight wire, circular loop and long solenoid.
  • 2.3.2 Integral forms of Maxwell's equations: Gauss' law (for E- and B-fields); Ampere's law; Faraday's law; using these laws for the calculation of fields when the integrand is almost piecewise constant. Boundary conditions for the electric field (or electrostatic potential) at the surface of conductors and at infinity; concept of grounded conductors. Superposition principle for elec­tric and magnetic fields; uniqueness of solution to well- posed problems; method of image charges.
  • 2.3.3 Interaction of matter with electric and magnetic fields; Resistivity and conductivity; differential form of Ohm's law. Dielectric and magnetic permeability; relative per­mittivity and permeability of electric and magnetic ma­terials; energy density of electric and magnetic fields; fer­romagnetic materials; hysteresis and dissipation; eddy currents; Lenz's law. Charges in magnetic field: helicoidal motion, cyclotron frequency, drift in crossed E- and B-fields. Energy of a magnetic dipole in a magnetic field; dipole moment of a current loop.
  • 2.3.4 Circuits: Linear resistors and Ohm's law; Joule's law; work done by an electromotive force; ideal and non-ideal batter­ies, constant current sources, ammeters, voltmeters and ohmmeters. Nonlinear elements of given V-I charac­teristic. Capacitors and capacitance (also for a single electrode with respect to infinity); self-induction and in­ductance; energy of capacitors and inductors; mutual in­ductance; time constants for RL and RC circuits. AC circuits: complex amplitude; impedance of resistors, in­ductors, capacitors, and combination circuits; phasor di­agrams; current and voltage resonance; active power.
Members of the Spanish National Team can download the course notes here:
Some cognitive conflicts involving Electromagnetism:
It is also useful to follow the IPhO's Study Guide by Jaan Kalda
Here you can find the solutions to some of the problems:

Preparation for the International Physics Olympiad (IPhO): Relativity

The IPhO Syllabus includes:
  • 2.5 Relativity: Principle of relativity and Lorentz transformations for the time and spatial coordinate, and for the energy and momentum; mass-energy equivalence; invariance of the spacetime interval and of the rest mass. Addition of par­allel velocities; time dilation; length contraction; relativ­ity of simultaneity; energy and momentum of photons and relativistic Doppler effect; relativistic equation of motion; conservation of energy and momentum for elas­tic and non-elastic interaction of particles.
Members of the Spanish National Team can download the notes here:
To know more:
Some cognitive conflicts involving Relativity:
It is also useful to follow the IPhO's Study Guide by Siim Ainsaar:
Here you can find the solutions to some of the problems:

Preparation for the International Physics Olympiad (IPhO): Thermodynamics and Statistical Physics

The IPhO Syllabus includes:

2.7 Thermodynamics and statistical physics
  • 2.7.1 Classical thermodynamics: Concepts of thermal equilibrium and reversible pro­cesses; internal energy, work and heat; Kelvin's tem­perature scale; entropy; open, closed, isolated systems; first and second laws of thermodynamics. Kinetic the­ory of ideal gases: Avogadro number, Boltzmann factor and gas constant; translational motion of molecules and pressure; ideal gas law; translational, rotational and os­cillatory degrees of freedom; equipartition theorem; in­ternal energy of ideal gases; root-mean-square speed of molecules. Isothermal, isobaric, isochoric, and adiabatic processes; specific heat for isobaric and isochoric pro­cesses; forward and reverse Carnot cycle on ideal gas and its efficiency; efficiency of non-ideal heat engines.
  • 2.7.2 Heat transfer and phase transitions: Phase transitions (boiling, evaporation, melting, subli­mation) and latent heat; saturated vapour pressure, rel­ative humidity; boiling; Dalton's law; concept of heat conductivity; continuity of heat flux.
  • 2.7.3 Statistical physics: Planck's law (explained qualitatively, does not need to be remembered), Wien's displacement law; the Stefan- Boltzmann law.
Members of the Spanish National Team can download the notes here:
Some cognitive conflicts involving Thermodynamis and Statistical Physics:
It is also useful to follow the IPhO's Study Guide by Jaan Kalda:
Here you can find the solutions to some of the problems: