Hi i am confuse about this answer Why do we differentiate by

Hi, i am confuse about this answer. Why do we differentiate by the p term in (d/dp) , which one is constant given the equation H=U+pV and why (du/dv)(dv/dp)=0 in the answer below. It would be good if you can go through with me step by step. Thank :)

Solution

p is not a constant .

It is the pressure with which we differentiate the gas law equation.PV = nRT.

where P is pressure V is volume and n - no of moles of gas/fluid and T is the temperature .

In the above equation H is enthalpy and U is the internal energy of the system.

Four quantities called \"thermodynamic potentials\" are useful in the chemical thermodynamics of reactions and non-cyclic processes. They are internal energy, the enthalpy, the Helmholtz free energy and the Gibbs free energy. Enthalpy is defined by

H = U + PV

where P and V are the pressure and volume, and U is internal energy. Enthalpy is then a precisely measurable state variable, since it is defined in terms of three other precisely definable state variables. It is somewhat parallel to the first law of thermodynamics for a constant pressure system

Q = U + PV since in this case Q=H

It is a useful quantity for tracking chemical reactions. If as a result of an exothermic reaction some energy is released to a system, it has to show up in some measurable form in terms of the state variables. An increase in the enthalpy H = U + PV might be associated with an increase in internal energy which could be measured by calorimetry, or with work done by the system, or a combination of the two.

The internal energy U might be thought of as the energy required to create a system in the absence of changes in temperature or volume. But if the process changes the volume, as in a chemical reaction which produces a gaseous product, then work must be done to produce the change in volume. For a constant pressure process the work you must do to produce a volume change V is PV. Then the term PV can be interpreted as the work you must do to \"create room\" for the system if you presume it started at zero volume.