Entropy and Specific heat

The SI unit for both specific heat and entropy is J?kg^?1?K^?1. But they do not signify the same thing. But they are not the same things.

First, let me sort out a big confusion of heat capacity vs specific heat.

Extensive property vs Intensive property

Heat capacity is defined as the amount of heat energy required to raise the temperature of a given quantity of matter by one degree Celsius.

Specific heat is the quantity of heat required to raise the temperature of one gram of a substance by one Celsius degree.

Therefore, the specific heat is more specific about the mas of substance that stands at 1 gram.

This is not a small difference.

Heat capacity is an extensive property. As a reminder, an extensive property of a substance is one where QUANTITY does matter.

Specific heat is an intensive property. Its magnitude does not depend upon the amount of matter present in the system. It is Q = m Cp dt, Cp = Q/ m x dt. It is the heat required to raise the temperature of 1 gram mass by 1 degc. It is not mass-dependent. The specific heat of 1 gram copper is the same as 1 kg copper. Specific heat depends on the inner character of a material and is specific to a material.

Entropy

Entropy opposite to specific heat is an extensive property.?As entropy changes with the size of the system hence it is an extensive property.

Explanation

What is specific heat?

A substance cannot increase its temperature until it has met the energy demand of its molecules. In other words, the energy supply to molecules is pre-taxed at the source before the substance has internally reached thermal equilibrium. A substance can increase its temperature only when internally it is in a state of thermal equilibrium. Every substance has different types of molecules, different numbers of molecules, and different arrangements of molecules; therefore, every substance has its own demand for a certain quantity of heat [energy] to reach internal thermal equilibrium, therefore, every substance offers resistance to heat transfer until its energy demand has been met before increasing temperature. This resistance to heat transfer is the specific heat.

A molecule can take only as much heat as it can store. The way a molecule stores its energy is the way the atoms in the molecule can arrange – the degree of freedom. There are three types of motions atoms possess in a molecule [ 1] translational [2] vibration and [3] rotation. Heat received by a molecule is equally dived and each mode of motion gets ? Kt energy. K is Boltzmann constant. Out of the three modes of motion, only translational motion raises the temperature while the others just consume energy. Therefore, we can redefine specific heat as a measure of kinetic energy. While the average kinetic energy of a molecule is the same for all gases and depends only on temperature, The kinetic energy per unit mass per unit kelvin is what you measure as specific heat and express it as Kj/kg/k.

Entropy

Entropy is a measure of the unavailability of that heat energy to do work. It is measured in joules/kg/ kelvin.

The increase in entropy of a system, dS, is given by dS = delta Q/T, where delta Q is heat transfer and T is the absolute temperature. The fundamental equation of entropy S is S= k ln W, where W is the number of ways of arranging the particles so as to produce a given state, and k is Boltzmann’s constant. The greater is W, the greater is S, more disorder. The unit of k is kJ/k and large values of W correspond to the most disordered states of the system, that is, the most random. So, S, the entropy of the system is a measure of how disordered the system is. The factor of k appears, to simplify our original formula, and it has the units of J/K. The more the delta Q per unit temperature the more is entropy. Thus, the unit of entropy is Kj/kg/k

Therefore, to summarize, the heat capacity of an object is the energy needed to increase the average kinetic energy of its molecules, which depends upon the number of KE modes that can absorb energy. Whereas, the increase in entropy for a given input of heat energy is a measure of the increase in disorder, due to that energy input. This depends on the absolute temperature, and the increase in disorder is inversely proportional to the temperature, for a given heat input. This explains why heat energy naturally flows from hot objects to colder objects

Entropy vs Specific heat data

The table below gives many data of specific heat vs entropy of many substances.

You will notice two things in the table below.

[1] All substances have different specific heat compared to the entropy

[2] Generally in both cases, the larger molecules have more specific heat and also more entropy

?The reasons are totally different. In the case of specific heat, it increases with atomicity or the degrees of freedom of atoms in a molecule like a diatomic gas has more specific heat than a monoatomic gas. In the case of entropy, more complex molecules have higher entropy because they have more bonds, which means they have more possible ways of rotating. Because they can rearrange themselves in various positions, they can take up more space.

Credit: Google