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To distinguish these two thermal expansion equations of state, the latter one is called pressure-dependent thermal expansion equation of state. To deveop the pressure-dependent thermal expansion equation of state, in an compression process at room temperature from (V 0, T 0, P 0) to (V 1, T 0,P 1), a general form of volume is expressed as
A number of materials contract on heating within certain temperature ranges; this is usually called negative thermal expansion, rather than "thermal contraction".For example, the coefficient of thermal expansion of water drops to zero as it is cooled to 3.983 °C (39.169 °F) and then becomes negative below this temperature; this means that water has a maximum density at this temperature, and ...
Defining equation SI unit Dimension Temperature gradient: No standard symbol K⋅m −1: ΘL −1: Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer P = / W ML 2 T −3: Thermal intensity I = / W⋅m −2
This concept lies in the basis for the kinetic theory of matter and thermal expansion of matter, which states as the temperature of a substance rises, so does the average kinetic energy of its molecules. As such, a rise in kinetic energy requires more space between the particles of a given substance, which leads to its physical expansion. [2]
is pressure, temperature, volume, entropy, coefficient of thermal expansion, compressibility, heat capacity at constant volume, heat capacity at constant pressure. Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials .
Many thermodynamic equations are expressed in terms of partial derivatives. For example, the expression for the heat capacity at constant pressure is: = which is the partial derivative of the enthalpy with respect to temperature while holding pressure constant.
The generalized force, X, corresponding to the external parameter x is defined such that is the work performed by the system if x is increased by an amount dx. E.g., if x is the volume, then X is the pressure. The generalized force for a system known to be in energy eigenstate is given by:
Each pair in the equation are known as a conjugate pair with respect to the internal energy. The intensive variables may be viewed as a generalized "force". An imbalance in the intensive variable will cause a "flow" of the extensive variable in a direction to counter the imbalance. The equation may be seen as a particular case of the chain rule.