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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 ...
For a single component system, the "standard" three parameters are the isothermal compressibility , the specific heat at constant pressure , and the coefficient of thermal expansion . For example, the following equations are true:
Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer P = / W ML 2 T −3: Thermal intensity I = / W⋅m −2: MT −3: Thermal/heat flux density (vector analogue of thermal intensity above) q
Since the isothermal compressibility is positive for nearly all phases, and the square of thermal expansion coefficient is always either a positive quantity or zero, the specific heat at constant pressure is nearly always greater than or equal to specific heat at constant volume: ,,.
The laws of thermodynamics imply the following relations between these two heat capacities (Gaskell 2003:23): = = Here is the thermal expansion coefficient: = is the isothermal compressibility (the inverse of the bulk modulus):
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 .
The first and second law of thermodynamics are the most fundamental equations of thermodynamics. They may be combined into what is known as fundamental thermodynamic relation which describes all of the changes of thermodynamic state functions of a system of uniform temperature and pressure.
A temperature coefficient describes the relative change of a physical property that is associated with a given change in temperature. For a property R that changes when the temperature changes by dT , the temperature coefficient α is defined by the following equation: