Energy and Thermodynamic Relations

Conservation of total energy is a law of mechanical systems, and it serves as the first law of fhermod5mamics. From the conservation of energy of a closed, isolated system, we can identify cerfain energy quantities that are state functions their values do not depend on the path the system followed to reach its current state. 

Problem Find an expression for the isothermal compressibility of a gas that obeys Equation 2.30, a Berthelot gas. 

Solution The isothermal compressibility, p in Equation 2.36, requires finding the derivative of V with respect to P at constant temperature. We start with the equation of state for the Berthelot gas. Equation 2.30. 

Substituting this into Equation 2.36 yields p for a Berthelot gas. 

This answer may be sufficient however, we could go back to the original equation of state and use it to express p in terms of only two variables, not three. From taking the inverse of the second form of the equation of state, 1/V is expressed in terms of P and T. 

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