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# What is the difference between entropy and enthalpy?

, ##H##, is the sum of internal energy ##U## of a system and the product of the pressure and change in volume of the system at a constant pressure.

, ##S##, is a measure of the disorder or randomness of a system.

ENTHALPY

##H = U + PV##

The ##PV## term represents the mechanical work done on or by the system, and is opposite in sign to the ##PV##-work term present within the first law of thermodynamics, ##DeltaU = q + w##.

Since we are usually more interested in changes than in absolute values, we can write

##DeltaH = DeltaU + PDeltaV##

I.e., the change in enthalpy is the sum of the change in the internal energy and the work done, at constant pressure (if it wasn't, we would have ##DeltaH = DeltaU + PDeltaV + VDeltaP##).

Example:

What is the change in enthalpy in a reaction under lab bench conditions (constant pressure) if it releases ##"100 kJ"## of internal energy and the system expands in such a way that ##PDeltaV = "10 kJ"##?

Solution:

##DeltaH = DeltaU + PDeltaV = -"100 kJ + 10 kJ" = -"90 kJ"##

ENTROPY

Entropy, ##S##, is a measure of the disorder or randomness of a system.

- An ordered system has low entropy. A disordered system has high entropy.

For example, in the solid state, molecules are strongly attracted to each other (less disorder).

In the gaseous state, molecules are not strongly attracted (more disorder). Because of that, entropy is greater in a gas.

##DeltaS## equals the heat transferred between the system and its surroundings divided by ##T##.

##DeltaS = q_"rev"/T = (ΔH)/T##

where the relationship ##q_"rev" = DeltaH## holds at constant pressure.

Enthalpy and entropy are different quantities. Enthalpy has the units of heat, joules. Entropy has the units of heat divided by temperature, joules per kelvin.

Check this to know more about enthalpy.