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In chemistry, the lever rule is a formula used to determine the mole fraction (x i) or the mass fraction (w i) of each phase of a binary equilibrium phase diagram.It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line.
On the Equilibrium of Planes (Ancient Greek: Περὶ ἐπιπέδων ἱσορροπιῶν, romanized: perí epipédōn isorropiôn) is a treatise by Archimedes in two books. The first book contains a proof of the law of the lever and culminates with propositions on the centre of gravity of the triangle and the trapezium.
Lever: The beam shown is in static equilibrium around the fulcrum. This is due to the moment created by vector force "A" counterclockwise (moment A*a) being in equilibrium with the moment created by vector force "B" clockwise (moment B*b). The relatively low vector force "B" is translated in a relatively high vector force "A".
There are two books to On the Equilibrium of Planes: the first contains seven postulates and fifteen propositions, while the second book contains ten propositions. In the first book, Archimedes proves the law of the lever, which states that: Magnitudes are in equilibrium at distances reciprocally proportional to their weights.
Thus, we wish to show that if the weight of the cross-section HE rests at G and the weight of the cross-section EF of the section of the parabola rests at J, then the lever is in equilibrium. In other words, it suffices to show that EF :GD = EH :JD. But that is a routine consequence of the equation of the parabola.
The phase diagram shows, in pressure–temperature space, the lines of equilibrium or phase boundaries between the three phases of solid, liquid, and gas. The curves on the phase diagram show the points where the free energy (and other derived properties) becomes non-analytic: their derivatives with respect to the coordinates (temperature and ...
Archimedes' interests in the conditions of stability for solid bodies are found both here and in his studies of the lever and centre of gravity in On the Equilibrium of Planes I-II. Book one of On Floating Bodies begins with a derivation of the Law of Buoyancy and ends with a proof that a floating segment of a homogeneous solid sphere is always ...
The lever is a movable bar that pivots on a fulcrum attached to or positioned on or across a fixed point. The lever operates by applying forces at different distances from the fulcrum, or pivot. The location of the fulcrum determines a lever's class. Where a lever rotates continuously, it functions as a rotary second-class lever.