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Isothermal processes are of special interest for ideal gases. This is a consequence of Joule's second law which states that the internal energy of a fixed amount of an ideal gas depends only on its temperature. [4] Thus, in an isothermal process the internal energy of an ideal gas is constant.
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
The reciprocal of the bulk modulus at fixed temperature is called the isothermal compressibility. Definition ... For an ideal gas, an isentropic process has: ...
The ideal gas model has been explored in both the Newtonian dynamics (as in "kinetic theory") and in quantum mechanics (as a "gas in a box"). The ideal gas model has also been used to model the behavior of electrons in a metal (in the Drude model and the free electron model), and it is one of the most important models in statistical mechanics.
Though the compression/heating process of solids can be constant temperature , and constant pressure (isobaric), it can not be a constant volume (isochoric), At high P-T, the pressure for the ideal gas is calculated by the force divided by the area, while the pressure for the solid is calculated from bulk modulus (K, or B) and volume at room ...
The Helmholtz free energy is defined as [3], where . F is the Helmholtz free energy (sometimes also called A, particularly in the field of chemistry) (SI: joules, CGS: ergs),; U is the internal energy of the system (SI: joules, CGS: ergs),
Isothermal : The process is at a constant temperature during that part of the cycle (=, =). Energy transfer is considered as heat removed from or work done by the system. Energy transfer is considered as heat removed from or work done by the system.
The process begins with gas under some pressure, ... For an ideal gas, ... is the same as for isothermal expansion where all heat is converted to work: ...