# Basic Concept of Specific Heats, Joule’s law and Enthalpy

## What is specific Heat?

The specific heat of a solid or liquid is defined as the amount of heat per unit mass required to a one-degree Celsius temperature rise. for small quantities, we have

where

• m : mass of the substance
• c : Specific Heat
• dT : Change of temperature in degree Celcius

### Specific heats for gases

For the gases, There are two kinds of specific heats are defined i.e.

Specific heat at constant pressure :

Specific Heat at constant volume :

So, we have

for reversible non flow process at constant pressure.

and

for reversible non flow process at constant volume.

The value of and is constant for a perfect gas at all pressure and temperature.

so, integrating equations   and , we have

flow of heat in a reversible constant pressure process:

flow of heat in a reversible constant volume process:

“In case of real gases, and vary with temperature.”

### The ratio of Specific Heats

The ratio of specific heat at constant pressure to the specific heat at constant volume is represented by symbol “γ”( Gamma).

So

Since, , it is clear that must be greater than for any perfect gas. So the ratio is always greater than 1.

### The relationship between two specific Heats

Let us consider a perfect gas being heated at constant pressure from to .

According to the closed system or non-flow equation,

Also, for a perfect gas,

…..(1)

In a constant pressure process, the work-done by the fluid,

Since, from the perfect gas equation , so and and in this case.

So, From equation (1), We have

…..(a)

But for a constant pressure process,

……(b)

By comparing equations (a) and (b), we have

or                     ….(2)

Dividing by c_v on both sides

Similarly, dividing both sides by , we get

## What is Joule’s Law?

Joule’s Law: “The internal energy of the perfect gas is a function of the absolute temperature only.”

i.e.

Let 1 kg of a perfect gas be heated at constant volume, according to the non-flow energy equation

since volume is constant i.e. work-done dW = 0

At constant volume for 1 kg of  perfect gas, we have

After integrating

where, K = constant

According to joule’s law that mean internal energy varies linearly with absolute temperature. Internal energy can be made zero at any similar reference temperature. It may be assume that u =0 when T = 0 for a perfect gas so constant K is zero.

i.e., Internal Energy, for a perfect gas

or Internal Energy

for a perfect gas, in any process between state 1 to state 2, we have from equation

Gain in internal energy,

So the gain of internal energy for a perfect gas between two states for any process, Reversible or irreversible.

## What is Enthalpy?

“One of the fundamental quantities which occur invariably in thermodynamics is the sum of internal energy (u) and pressure-volume product (p.v). This sum is called Enthalpy.” Enthalpy is denoted by “h”.

i.e.

The enthalpy of a fluid is the property of the fluid since it consists of the sum of property and the product of two properties. Since enthalpy is a property like internal energy, pressure, specific volume and temperature, it can be introduced into any problem whether the process is a flow or a non-flow process.

The total enthalpy of mass, m, of a fluid can be

where

H = m.h

For a perfect gas:

Since

Since

i.e.

it is assumed that u = 0 at T = 0 then h = 0 at T = 0.