Joule's Law

    

Joule's Law of Heating Formula
\( q \;=\; I^2 \cdot R \cdot t \)     (Joule's Law of Heating) \( I \;=\; \sqrt{ \dfrac{ q }{ R \cdot t } } \) \( R \;=\; \dfrac{ q }{ I^2 \cdot t }\)  \( t \;=\; \dfrac{ q }{ I^2 \cdot R} \)
Symbol	English	Metric
\( q \) = Heat	\(Btu\;/\;lbm\)	\(kJ\;/\;kg\)
\( I \) = Current	\(A\)	\(C\;/\;s\)
\( R \) = Resistance	\(\Omega\)	\(kg-m^2\;/\;s^3-A^2\)
\( t \) = Time Duration	\(sec\)	\(s\)

Joule's laws refer to several principles in physics, particularly in the realm of thermodynamics and electricity.  These laws have been instrumental in understanding and formulating various principles in physics, particularly in the study of energy conversion and thermodynamics.

Main Joule's Laws

Joule's Law of Heating  -  This law relates the amount of heat produced by a electric current passing through a resistor and the electrical power supplied.  This law essentially states that the heat produced in a resistor is directly proportional to the square of the current passing through it, the resistance of the resistor, and the time for which the current flows.
Joule's First Law  -  This law relates the internal energy of a gas to its temperature change.  It states that the internal energy of an ideal gas is directly proportional to its absolute temperature.  This law is a specific application of the more general principle of conservation of energy.
Joule's Second Law  -  Also called Joule's law of work and heat, this law states that the internal energy of an ideal gas remains constant if it undergoes an adiabatic process (a process where there is no transfer of heat between the system and its surroundings).  This law essentially says that no work is done on or by the gas, and no heat is transferred to or from the gas, then the internal energy remains constant.

There is also some ambiguity regarding the specific "laws" attributed to James Prescott Joule.  While the term Joule's laws is often used to refer to the principles I previously mentioned, it's worth noting that Joule himself did not explicitly formulate a set of laws bearing his name.  Joule made significant contributions to the fields of thermodynamics, electricity, and energy, and several principles and laws are associated with his work.

Joule's First Law Formula
\( \mu \;=\; \dfrac{ \Delta T }{ \Delta p } \)     (Joule's First Law) \( \Delta T \;=\; \mu \cdot \Delta p \) \( \Delta p \;=\; \dfrac{ \Delta T }{ \mu } \)
Symbol	English	Metric
\( \mu \) (Greek symbol mu) = Joule-Thomson Coefficient	\(dimensionless\)	\(dimensionless\)
\( \Delta T \) = Temperature Change	\(F\)	\(K\)
\( \Delta p \) = Pressure Change	\(lbf \;/\; in^2\)	\(Pa\)

 In Addition to Those Mentioned Above, Here are a Few More Principles Closely Associated with Joule

Joule's Law of Work Done in Magnetization  -  Joule discovered that when a magnetic material is magnetized, mechanical work is done, and heat is generated.  This principle laid the foundation for understanding the relationship between magnetic fields and energy.
Joule-Thomson Effect  -  Although William Thomson (Lord Kelvin) was also involved, Joule's experiments with expanding gases contributed to the understanding of the Joule-Thomson effect.  This effect describes the change in temperature of a gas when it is forced through a valve or porous plug while kept insulated, without the transfer of heat between the gas and its surroundings.
Joule's Experiments on Conservation of Energy  -  Joule conducted experiments demonstrating the mechanical equivalent of heat, which was crucial in establishing the principle of conservation of energy.  This work led to the understanding that energy can be converted from one form to another but is never created or destroyed.

While these principles are associated with Joule's work, it's important to recognize that the term "Joule's laws" is not as precisely defined as, for example, Newton's laws of motion or the laws of thermodynamics.  Instead, Joule's contributions span various areas of physics and are encapsulated in several principles and concepts.

Joule's Second Law Formula
\( U \;=\;\) constant
Symbol	English	Metric
\( U \) = Gas Internal Energy	\(constant\)	\(constant\)