![]() This gives an expression for internal energy that is consistent with equipartition of energy. Then making use of the definition of temperature in terms of entropy: To apply this definition of temperature to a monoatomic ideal gas, we need an expression for the entropy of an ideal gas: This form of the temperature can be obtained from the thermodynamic identity. This is certainly not as intuitive as molecular kinetic energy, but in thermodynamic applications it is more reliable and more general. Temperature is expressed as the inverse of the rate of change of entropy with internal energy, with volume V and number of particles N held constant. ![]() But in view of practical difficulties with that approach, temperature is often defined in terms of two other state variables, entropy S and internal energy U. The definition of temperature in terms of molecular kinetic energy, the " kinetic temperature", is commonly used in introductory treatments of thermodynamics. The Relationship of Entropy to Temperature Noting that the equilibrium state of a collection of particles will be the state of greatest multiplicity, then one can define the temperature in terms of that multiplicity (entropy) as follows: In that case the equilibrium reached is one of maximum entropy, and the rate of approach to that state will be proportional to the difference in temperature between the two parts of the system. The kinetic temperature for monoatomic ideal gases described above is consistent with this definition of temperature for the simple systems to which it applies. ![]() When two objects are in thermal contact, the one that tends to spontaneously lose energy is at the higher temperature." (Thermal Physics, Ch 1.)
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