Thermodynamics The equations of state

The internal energy of a system or body (for example, a unit of air volume) with well-defined boundaries, denoted by U, is the total kinetic energy due to the motion of particles (translational, rotational and vibrational) and the potential energy associated with the vibrational and electric energy of atoms within molecules or any matter state. This includes the energy in all chemical bonds and that of free electrons (for example, hydrated electrons in water and photons in air). 

In the gas phase, work is carried out primarily as pressure-volume work (in the condensed phase such as droplets and solid particles, surface work, electrical work and expansion work also occur). The change of volume occurs at a constant pressure (isobaric change of state) and so it is valid that 

If no other work is carried out, the differential change of internal energy is described by 

98 °C per 100 m this is called the dry adiabatic lapse rate (DALR), or dTldz. As soon as the air parcel is saturated by water vapor, it partly condenses and is then heated by the released heat. Then, the wet adiabatic temperature gradient (lapse rate) is observed, which lies between 0.4 °C at large temperatures and 1 °C for low temperatures. During adiabatic changes, the potential tew/jeramrc remains constant, 

The heat needed to heat one mole of a gas at constant volume is called molar heat capacity C, it is defined as g = CvAT. The temperature dependency of Cv is  

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