Energy input to a system

The total energy of a group of particles of the same species can be written  

The variation in this energy, during a reversible transformation, will have the form  

Note that a modification in the total energy of a group is due to two factors  

When a system is heated, the energy levels e, are unchanged but their population , is modified. When the system exchanges work, this time the 

As we have just seen, when a system is heated at a constant voliune, the energy levels do not vary therefore, without any modification other than heating, the variation in energy of the ensemble will be given by the heat involved in a reversible transformation, which corresponds to the first term in the second part of eqitation [4.32]  

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