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# Thermodynamic Quantity: Enthalpy

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#### Thermodynamic Quantity: Enthalpy - Lesson Summary

To study the heat changes in a chemical reaction at constant temperature and constant pressure, a new thermodynamic function called enthalpy was introduced.

The total heat content of a system at constant pressure is equal to the sum of the internal energy and PV. This is called the enthalpy of a system which is represented by H.

Note that enthalpy is also called as heat content.
H = U + pv

Enthalpy which depends on the three state functions: internal energy, pressure and volume.Hence it is also a state function.

Enthalpy of a substance cannot be measured, but change in enthalpy can be measured.
Change in enthalpy =  Enthalpy of products - Enthalpy of reactants
âˆ†H = H P-H R
From the first law of thermodynamics
âˆ†U =qp-Pâˆ†V
qp =heat absorbed by the system
-Pâˆ†V=work done by the system.
For finite changes at constant pressure,
âˆ†H= âˆ†U+âˆ†(PV)
âˆ†H=âˆ†U+Pâˆ†V         (âˆµ P is constant )
âˆ†H=qp
âˆ†H=-Ve for exothermic reactions
âˆ†H=+Ve for endothermic reactions.

Relation between âˆ†H &âˆ†U:
Solids and liquids do not show significant change in the volume when heated. Thus if change in volume, âˆ†V is insignificant
âˆ†H=âˆ†U+Pâˆ†V
âˆ†H=âˆ†U+P(0)
âˆ†H=âˆ†U

The difference between the change in internal energy and enthalpy becomes significant when gases are involved in the reaction.
Consider a chemical reaction occurring at constant temperature, T and constant pressure, P. Let the volume of the reactants is V A and the number of moles in the reactants is n A. Similarly, the volume of the products is V B and the number of moles in the product is n B.
According to the ideal gas equation,
Pv=nRT
pv A=n ART
pv B= n BRT
Thus
pv B- pv A = n BRT- n ART
p(v B- v A) =RT(n B-n A)
pâˆ†v =âˆ†n gRT
âˆ†H=âˆ†U +pâˆ†v
âˆ†H=âˆ†U+âˆ†n gRT

Heat capacity:  The capacity to absorb heat energy and store it is known as the heat capacity of a system.
q=C .âˆ†T
Where C is called the heat capacity of the system.
If q calories is the heat absorbed by the mass m and the temperature rises from T 1 to T 2, the heat capacity
C is given by the expression
C = q /T 2-T 1
Thus, heat capacity is defined as the amount of heat required by unit mass to raise the temperature of the system by one degree at a specified temperature. This is also known as specific heat capacity.
The SI units of molar heat capacity are J0k-1mole-1.

Relation between molar heat capacity at constant volume, which is denoted by Cv and molar heat capacity at constant pressure, which is denoted by Cp:

q=Câˆ†v
At constant volume
q v=C vâˆ†T =âˆ†U
At constant pressure
q p = C pâˆ†T =âˆ†H
The difference between Cp and CV for one mole of an ideal gas can be derived as follows:
The change in enthalpy for one mole of an ideal gas âˆ†H= âˆ†U+âˆ†(PV)
For 1 mole of gas pv =RT
âˆ†H= âˆ†U+âˆ†(RT)
R is aconstant
âˆ†H= âˆ†U+Râˆ†T
C pâˆ†T= C vâˆ†T+Râˆ†T
Since  âˆ†T=1
C p= C +R
R = C p- C v