In such conditions, Ohm's law states that the current is directly proportional to the potential difference between two ends ( across ) of that metal ( ideal ) resistor ( or other ohmic device ):

The behavior of an ideal resistor is dictated by the relationship specified by Ohm's law:

When applied to harmonic regimes, this formality is similar to Ohm's Law in ideal AC circuits.

When applied to harmonic regimes, this formality is similar to Ohm's Law in ideal AC circuits.

Such temperature changes can be quantified using the ideal gas law, or the hydrostatic equation for atmospheric processes.

We can solve for the temperature of the compressed gas in the engine cylinder as well, using the ideal gas law.

Differentiating Equation ( 3 ) and use of the ideal gas law,, yields

Using the ideal gas law and assuming a constant molar quantity ( as often happens in practical cases ),

The ideal gas law or another equation of state is often used in conjunction with these equations to form a determined system to solve for the unknown variables.

In accordance to Avogadro's law this volume is the same for all ideal gases, which is 22. 414 liters at standard temperature and pressure.

Introducing the ideal gas law per unit volume for the osmotic pressure, the formula becomes identical to that of Einstein's.

The green curve uses the general pressure law for an ideal Fermi gas, while the blue curve is for a non-relativistic ideal Fermi gas.

One of the simplest equations of state for this purpose is the ideal gas law, which is roughly accurate for weakly polar gases at low pressures and moderate temperatures.

In 1834 Émile Clapeyron combined Boyle's Law and Charles ' law into the first statement of the ideal gas law.

According to Avogadro ’ s law this volume is same for all ideal gases and if we consider ‘ n ’ moles of an ideal gas at STP, then the equation becomes

The classical ideal gas law may be written:

The ideal gas law may also be expressed as follows

Proposed in 1873, the van der Waals equation of state was one of the first to perform markedly better than the ideal gas law.

While the equation is definitely superior to the ideal gas law and does predict the formation of a liquid phase, the agreement with experimental data is limited for conditions where the liquid forms.

The van der Waals equation may be considered as the ideal gas law, “ improved ” due to two independent reasons:

We see this as diminishing of pressure on the outer shell ( which is used in the ideal gas law ), so we write ( something ) instead of.

General equilibrium theory has demonstrated, with varying degrees of mathematical rigor over time, that under certain conditions of competition, the law of supply and demand predominates in this ideal free and competitive market, influencing prices toward an equilibrium that balances the demands for the products against the supplies.

Some eight decades later, Isaac Newton proved that relationships like Kepler's would apply exactly under certain ideal conditions that are to a good approximation fulfilled in the solar system, as consequences of Newton's own laws of motion and law of universal gravitation.

If the air density and temperature are the same above and below a wing, a naive application of the ideal gas law requires that the pressure also be the same.

Pressure varies linearly with temperature, volume, and quantity according to the ideal gas law,

If internal responsibility suggests acceptance of the socialist ideal of equality, then external responsibility implies adherence to principles of ideological supranationalism.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

For an adiabatic free expansion of an ideal gas, the gas is contained in an insulated container and then allowed to expand in a vacuum.

For an ideal I, if a ∉ I and-a ∉ I, then I ∪

While the British military historian Sir John Keegan suggested an ideal definition of battle as " something which happens between two armies leading to the moral then physical disintegration of one or the other of them ", the origins and outcomes of battles can rarely be summarized so neatly.

Let A be a unital commutative Banach algebra over C. Since A is then a commutative ring with unit, every non-invertible element of A belongs to some maximal ideal of A.

then there are elements x and y in R such that ax + by = d. The reason: the ideal Ra + Rb is principal and indeed is equal to Rd.

If the ideals A and B of R are coprime, then AB = A ∩ B ; furthermore, if C is a third ideal such that A contains BC, then A contains C. The Chinese remainder theorem is an important statement about coprime ideals.

In fact, if I is a nonzero ideal of R then any element a of I

In a ring all of whose ideals are principal ( a principal ideal domain or PID ), this ideal will be identical with the set of multiples of some ring element d ; then this d is a greatest common divisor of a and b. But the ideal ( a, b ) can be useful even when there is no greatest common divisor of a and b. ( Indeed, Ernst Kummer used this ideal as a replacement for a gcd in his treatment of Fermat's Last Theorem, although he envisioned it as the set of multiples of some hypothetical, or ideal, ring element d, whence the ring-theoretic term.

" And then they went to work and elaborated this one principle all through, and it is a most wonderful ideal: how all that we call ethics they simply bring out from that one great principle of non-injury and doing good.

In this sense it is the western view of the Holy Grail which comes closest to the Sufic ideal ; for to the Sufis Perfection is the Grail ; and the Holy Grail is for those who after they become perfect by giving all they have to the poor then go on to become " Abdal " or " changed ones " like Enoch who was " taken " by God because he " walked with God ".

In particular, Ribbentrop acquired the habit of listening carefully to what Hitler was saying, memorizing the Führer's pet ideas, and then later presenting Hitler's ideas as his own – a practice that much impressed Hitler as proving Ribbentrop was an ideal National Socialist diplomat.

There are various method employed to " cast on ," such as the " thumb method " ( also known as " slingshot " or " long-tail " cast-ons ), where the stitches are created by a series of loops that will, when knitted, give a very loose edge ideal for " picking up stitches " and knitting a border ; the " double needle method " ( also known as " knit-on " or " cable cast-on "), whereby each loop placed on the needle is then " knitted on ," which produces a firmer edge ideal on its own as a border ; and many more.

then I is called an ideal in the Lie algebra.

Let then the record be written with sincerity and care ; thus with practice it will be found more and more to approximate to the ideal.

If that ideal size is large enough to supply the whole market, then that market is a natural monopoly.