The first law of thermodynamics states that in a thermodynamic system, the total energy consisting of internal heat energy as well as mechanical energy is conserved. The internal energy of a closed system, U, is a single-valued function of the independent thermodynamic variables, V and T, and, as such, its variation must be a perfect differential, because, otherwise, there will be a mechanism to create new energy. So, we may write dU = (dU/dV)xdV +(dU/dT)ydT (3.2.1)
Now, if a quantity of heat §Q be supplied to the closed system, it will go to increase. the existing internal energy by dU and do work by increasing the volume by dV against external pressure p on the system. Here it should be noted that §Q is not a perfect differential like dV, or dT, or dU. So, we may write,
The Eq. (3.2.2), therefore, is a mathematical statement of the First Law of thermodynamics.
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