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Thus, indirectly, thermal velocity is a measure of temperature. Technically speaking, it is a measure of the width of the peak in the Maxwell–Boltzmann particle velocity distribution . Note that in the strictest sense thermal velocity is not a velocity , since velocity usually describes a vector rather than simply a scalar speed .
q = Heat per unit mass added into the system. Strictly speaking, enthalpy is a function of both temperature and density. However, invoking the common assumption of a calorically perfect gas, enthalpy can be converted directly into temperature as given above, which enables one to define a stagnation temperature in terms of the more fundamental property, stagnation enthalpy.
Bernoulli's principle is a key concept in fluid dynamics that relates pressure, density, speed and height. Bernoulli's principle states that an increase in the speed of a parcel of fluid occurs simultaneously with a decrease in either the pressure or the height above a datum. [1]:
So cool air lying on top of warm air can be stable, as long as the temperature decrease with height is less than the adiabatic lapse rate; the dynamically important quantity is not the temperature, but the potential temperature—the temperature the air would have if it were brought adiabatically to a reference pressure. The air around the ...
The temperature approaches a linear function because that is the stable solution of the equation: wherever temperature has a nonzero second spatial derivative, the time derivative is nonzero as well. The heat equation implies that peaks ( local maxima ) of u {\displaystyle u} will be gradually eroded down, while depressions ( local minima ...
When stated in terms of temperature differences, Newton's law (with several further simplifying assumptions, such as a low Biot number and a temperature-independent heat capacity) results in a simple differential equation expressing temperature-difference as a function of time. The solution to that equation describes an exponential decrease of ...
The potential temperature of a parcel of fluid at pressure is the temperature that the parcel would attain if adiabatically brought to a standard reference pressure , usually 1,000 hPa (1,000 mb). The potential temperature is denoted θ {\displaystyle \theta } and, for a gas well-approximated as ideal , is given by
That is, when a system is described by stating its internal energy U, an extensive variable, as a function of its entropy S, volume V, and mol number N, i.e. U = U (S, V, N), then the temperature is equal to the partial derivative of the internal energy with respect to the entropy [59] (essentially equivalent to the first TdS equation for V and ...