# Enthalpy vs Entropy

Enthalpy and Entropy are two significant thermodynamic quantities. Understanding these quantities and how they change in specific processes allow us to infer the heat of reaction, the feasibility of the reaction, the temperature of the system, etc. So, let’s look at Enthalpy vs Entropy.

Index

## What is Enthalpy

Enthalpy, represented as H for a thermodynamic system, is the sum of the internal energy and the product of pressure and volume of the system.

$$H = U + PV$$

The product of pressure and volume also represents the work done on the system that produces such system dimensions.

The S.I. unit of enthalpy is the same as that of energy, i.e Joules(J).

The change in enthalpy is a more helpful quantity for practical purposes.

$$\Delta H = \Delta U + \Delta P V$$

Using the chain rule of differentiation,

$$\Delta H = \Delta U + P \Delta V + V \Delta P$$

If a reaction takes place at constant pressure, then $$\Delta P = 0$$ and,

$$\Delta H = \Delta U +P \Delta V = q$$ (Heat)

Hence, enthalpy represents the heat of an isobaric reaction.

## What is Entropy

Entropy, represented by $$S$$, can be defined in a handful of ways. In thermodynamics, Rudolf Clausius defined entropy as:

$$dS = \frac{dQ}{T}$$

If $$dQ$$ heat is added to a heat reservoir at an instantaneous temperature $$T$$, then their ratio represents the infinitesimal change in entropy $$dS$$.

The S.I. unit of entropy is Joule per Kelvin (J/K).

## History of Enthalpy vs Entropy

Now, let’s have a small glance at the history of enthalpy vs entropy and find out where these concepts came from.

### History of Enthalpy

Josiah Willard Gibbs used the concept of enthalpy to describe a heat function for constant pressure. Benoît Paul Émile Clapeyron and Rudolf Clausius introduced the concept of heat content and used the symbol $$H$$ for it. Heike Kamerlingh Onnes, who discovered superconductivity, coined the term ‘Enthalpy’ for this quantity in 1909.

### History of Entropy

Rudolf Clausius gave the first definition of entropy in 1865. Scientists like Ludwig Boltzmann, Josiah Willard Gibbs, and James Clerk Maxwell gave a statistical definition of the thermodynamic concept of Entropy.  Boltzmann argued that entropy is proportional to the natural logarithm of something known as the number of microstates the system can obtain (out of the current scope of discussion). The proportionality constant is the Boltzmann constant $$k_B$$.

## Enthalpy vs Entropy

Now, since we know what these two thermodynamic quantities are. Let’s have a look at the difference between enthalpy and entropy, i.e, enthalpy vs entropy.

## Similarities Between Enthalpy and Entropy

Both enthalpy and entropy are State Functions and depend only upon the initial and final conditions. Also, both are dependent upon temperature.

## FAQs

What is the third law of thermodynamics?

The third law of thermodynamics asserts that entropy is zero at zero Kelvin.

Why is Enthalpy dependent upon temperature?

Consider any gas. The internal energy of the gas is a function of the absolute temperature. Enthalpy depends upon the internal energy; therefore, enthalpy depends upon the temperature.

How are Enthalpy and Entropy related?

At constant pressure,
$$\Delta H = \Delta U +P \Delta V = q$$ (Heat)
and,
$$\Delta S = \frac{q}{T}$$
Where, $$q$$ was taken as small as possible.
So, we have,
$$\Delta S = \frac{\Delta H }{T}$$

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