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The internal energy depends only on the internal state of the system and not on the particular choice from many possible processes by which energy may pass into or out of the system. It is a state variable, a thermodynamic potential, and an extensive property. [5] Thermodynamics defines internal energy macroscopically, for the body as a whole.
Since the internal energy of the gas during Joule expansion is constant, cooling must be due to the conversion of internal kinetic energy to internal potential energy, with the opposite being the case for warming. Intermolecular forces are repulsive at short range and attractive at long range (for example, see the Lennard-Jones potential ...
The other equation of state of an ideal gas must express Joule's second law, that the internal energy of a fixed mass of ideal gas is a function only of its temperature, with = (,). For the present purposes it is convenient to postulate an exemplary version of this law by writing:
The above derivation uses the first and second laws of thermodynamics. The first law of thermodynamics is essentially a definition of heat, i.e. heat is the change in the internal energy of a system that is not caused by a change of the external parameters of the system.
That axiom stated that the internal energy of a phase in equilibrium is a function of state, that the sum of the internal energies of the phases is the total internal energy of the system, and that the value of the total internal energy of the system is changed by the amount of work done adiabatically on it, considering work as a form of energy.
The concept of internal energy and its relationship to temperature. If a system has a definite temperature, then its total energy has three distinguishable components, termed kinetic energy (energy due to the motion of the system as a whole), potential energy (energy resulting from an externally imposed force field), and internal energy. The ...
where W is work, U is internal energy, and Q is heat. [1] Pressure-volume work by the closed system is defined as: = where Δ means change over the whole process, whereas d denotes a differential. Since pressure is constant, this means that =. Applying the ideal gas law, this becomes
According to the assumptions of the kinetic theory of ideal gases, one can consider that there are no intermolecular attractions between the molecules, or atoms, of an ideal gas. In other words, its potential energy is zero. Hence, all the energy possessed by the gas is the kinetic energy of the molecules, or atoms, of the gas.