concerning heat and energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. A simple statement of the law is that heat always flows spontaneously from hotter to colder regions of matter (or 'downhill' in terms of the temperature gradient). Another statement is: "Not all heat can be converted into work in a cyclic process." These are info ... wherever there exists a difference of temperature, motive power can be produced. The production of motive power is then due in steam engines not to an actual consumption of caloric, but to its transportation from a warm body to a cold body ... The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperatures of the bodies between which is effected, finally, the transfer of caloric. In modern terms, Carnot's principle may be stated more precisely: where Wn is the net work done by the engine per cycle, qH > 0 is the heat added to the engine from a hot reservoir, and qC = −|qC| < 0 is waste heat given off to a cold reservoir from the engine. Thus the efficiency depends only on the ratio |qC| / |qH|. Carnot's theorem states that all reversible engines operating between the same heat reservoirs are equally efficient. Thus, any reversible heat engine operating between temperatures TH and TC must have the same efficiency, that is to say, the efficiency is a function of temperatures only:

purpose of modeling how a quantity such as heat diffuses through a given region. Since then, the heat equation and its variants have been found to be fundamental In mathematics and physics (more specifically thermodynamics), the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. Since then, the heat equation and its variants have been found to be fundamental in many parts of both pur Flowing u via. the heat equation causes it to become closer and closer as time increases to a steady-state solution. For very large time, u is closely approximated by a steady-state solution. A steady state solution of the heat equation is equivalently a solution of Laplace's equation. Similarly, a solution to the nonhomogeneous heat equation ∂ u ∂ t = ∇ 2 u + f … The time rate of temperature change at x is proportional to the heat flowing into an infinitesimal volume element, where the constant of proportionality is dependent on a constant κ ∂ t u ( x , t ) = κ ( x ) Q ( x , t ) {\displaystyle \partial _{t}u(x,t)=\kappa (x)Q(x,t)}