Joule’s law

Joule s law The internal energy of a gas depends only on its temperature (being independent of its pressure and volume). Like the other gas laws, it is only approximately true. At high pressures it is invalidated by the existence of inlermolecular forces. 

Joule s law The internal energy of a given quantity of gas depends only on its temperature and is independent of its pressure and volume. 

Joule believed that nature was ultimately simple, and strove to find the simple relationships (like Joule s law in electricity), which he was convinced must exist between important physical quantities. His phenomenal success in finding such relationships in the laboratory made a crucial contribution to... 

The law was stated in this form by J. P. Joule in 1844 it is usually referred to as AVoestyn s law (1848). It shows that the carriers of heat in a solid compound are not the molecules of the latter, but the atoms of its constituent elements. Joule s law enables one to calculate the molecular heats of compounds from the atomic heats of their elements, and the atomic heats of elements in the solid state when the latter are not readily directly accessible (solid oxygen, from c(CaC03) — c-(Ca) — c(C) = 3c(0), or 100 X 0 203 — 6 4 — P8 = 3 X 4 0). 

According to Joule s law ( 9), the molecular heat of a compound is the sum of the atomic heats of its components, and since this holds good even when the atomic heats are irregular, i.e., not equal to 6 4, it seems that the heat content of a solid resides in its atoms, and not in the molecular complexes as such. This agrees with Einstein s theory. Hence the molecular heat of a compound should be calculable by means of the formula ... 

During the next decades after the appearance of the Volta pile and of different other versions of batteries, fundamental laws of electrodynamics and electromagnetism were formulated based on experiments carried out with electric current supplied by batteries Ampere s law of interaction between electrical currents (1820), Ohm s law of proportionality between current and voltage (1827), the laws of electromagnetic induction (Faraday, 1831), Joule s law of the thermal effect of electric current, and many others. 

He is remembered for Joule s Law lhat describes the rale at which heal is produced by an electric current. Joule s work showed there were different kinds or energy, which can be changed into each other. He established the mechanical equivalence of heat. His work led to the law of conservation of energy. Alsu, he collaborated with William Thomson (Lord Kelvin) and verified experimentally the Joule-Thomson refrigeration effect. 

For an ideal gas the internal energy Udepends on the temperature T only (Joule s law) and the volume V is inversely proportional with the pressure p at constant temperature (Boyle s law). Equation 7.1 shows the equation of state for an ideal gas ... 

Work IF effected by current I on passage through resistance R in t seconds at a potential difference E is determined by Joule s law ... 

Equation (6.1) states that the internal energy is independent of volume at constant temperature, the usual statement of Joule s law. 

Instead of defining a perfect gas as we have done, by Boyle s law and Joule s law, we may prefer to assume that a thermodynamic temperature scale is known, and that the perfect gas satisfies the general gas law PV = const. X T. Then we can at once use the relation (6.2) to calculate the change of internal energy with volume at constant temperature, and find it to be zero. That is, we show directly by thermodynamics that Joule s lawr follows from the gas law, if that is stated in terms of the thermodynamic temperature. 

This is a reversal of the argument of Chap. II, Sec. 6, where we used Joule s law as an experimental fact to prove that the gas scale of temperature was identical with the thermodynamic temperature. Here instead we assume the temperature T in Eq. (1.1) to be the thermodynamic temperature, and then Joule s law follows as a thermodynamic consequence of the equation of state. 

A number of liquid elements and compounds containing n atoms in the molecule have molecular heats which are approximately additively composed of atomic heats of about 6 g-cal.," agreeing with -Dulong and Petit s law and Joule s law for solids ( 13,16.IX M) ... 

Joule s law states that an electric current produces in a circuit an amount of heat which is proportional to the square of the current intensity, to the resistance in the circuit, and to the duration of the current. The heat produced in the circuit is... 

Joule s law is strictly accurate so long as the conductor in which the evolution of heat is measured is homogeneous and at a uniform temperature throughout. If these conditions are not complied with, deviations from the law are obtained, and the evolution of heat is found to be no longer completely irreversible. By raising the temperature of certain parts of the circuit, electric currents can now be obtained. These reversible phenomena are called thermoelectrical phenomena in the more restricted sense of the term. In common with all other reversible processes, they must follow certain regularities, which are deter-... 

Resistively heated filament pyrolysers were used for a long time in polymer pyrolysis [9], A schematic drawing of a common filament pyrolyser is shown in Figure 4.1.1. The principle of this type of pyrolyser is that an electric current passing through a resistive conductor generates heat in accordance with Joule s law ... 

We define a perfect gas as any gas which obeys the following laws Joule s law the internal energy (u) per mole depends only upon the absolute temperature. The energy of n moles is therefore... 

According to Joule s law, power produced when current flows through a resistive medium is dissipated as heat. This heat increases in direct proportion to the resistance but in proportion to the square of the current. The reduction in resistance caused by a high ionic strength buffer therefore leads to increased current and excessive heat. These buffers yield sharper band separations, but the benefits of sharper resolution are diminished by the Joule (heat) effect that leads to denaturation of heat-labile proteins or degradation of other components. 

Now it has been shown that the internal energy of a perfect gas would be independent of the volume occupied, and would depend only on the temperature (Joule s Law) Hence, applying the above expression to the case of a perfect gas, in order to make dU independent of V, it isi necessary to consider—... 

If Boyle s Law (pv)T = constant and Joule s Law (U = KT) both held gold, then pv + U would depend on temperature only, 1 e would be uninfluenced by the volume change which necessarily takes place on passing from a high to a low pressure But (pv + U) is shown to be constant whether the gas laws are obeyed or not, and hence, if they were obeyed, T would necessarily be a constant likewise, that is, there would VOL II 5... 

Deviations from Boyle s Law—Heating or cooling produced according to the temperature and actual absolute pressure worked at Deviations fi om Joule s Law —Cooling in all cases The observed phenomena will be the resultant of these simultaneous effects... 

The quantity of heat developed in a conductor during the passage of an electric current of intensity C, for a short interval of time dt is given by the expression kC. dt (Joule s law), where k is a constant depending on the nature of the circuit. If the current remains constant during any short interval of time, the amount of... 

If the derivative of energy with respect to volume is zero, the energy is independent of the volume. This means that the energy of the gas is a function only of temperature. This rule of behavior is Joule s law, which may be expressed either by Eq. (7.22) or by 1/ = U(T). 

Later experiments, notably the Joule-Thomson experiment, have shown that Joule s law is not precisely correct for real gases. In Joule s apparatus the large heat capacity of the vat of water and the small heat capacity of the gas reduced the magnitude of the effect below the limits of observation. For real gases, the derivative (dU/dV) is a very small quantity, usually positive. The ideal gas obeys Joule s law exactly. 

---