The Kinetic energy theory helps us to understand what will happen to energy when we heat something. If you put a vessel full of water on a hot stove, you are going to make the molecules in the water move around more quickly and collide with each other. The more heat we supply, the molecules move faster, and these molecules start moving apart. Eventually, they collide around so much that they break apart from one another. At that point, the liquid you have been heating turns into a gas, your water becomes vapor and starts evaporating away. The heat can be transferred from one place to another in different ways:

•Conduction

•Convection

• Radiation

The volume of heat supplied to heat an object can be expressed as:

Q = C dt

where,

Q = amount of heat supplied (J, Btu)

The C= heat capacity of the system or object (J/K, Btu/ oF)

dt = temperature rise (K, °C, oF)

J/K (joule per kelvin) is the SI unit of heat capacity. In the system of English, the units are British thermal units per pound per degree Fahrenheit (Btu/oF).

The Specific Heat Capacity is the amount of heat required to change the temperature of a mass unit of an element by one degree. Specific heat is a more general term for the same.

The heat provided to a mass can be expressed as:

dQ = m c dt

There are two determinations of Specific Heat for gases and vapor:

Cp = (δh / δT) p - The specific Heat at constant pressure

Cv = (δh / δT)v - The specific Heat at constant volume

Gas Constant

R = C

The ratio of Specific Heat

K = C

The formula q = n C ∆T represents the heat required q to bring about the change in the ∆T variation in temperature of one mole of any kind of matter. C is the constant here it is called the molar heat capacity of the body. Thus, the capacity of the molar heat of any substance is determined as the amount of heat energy needed to change the temperature of 1 mole of that element by 1 unit. It depends on the type, quantity, and composition of the system.

There are two types of the molar heat capacity, that is, C

Derivation of Cp and Cv relation using ideal gases

From the equation q = n C ∆T, we can get,

At constant pressure CP, we get

qP = n CP∆T

This value is exactly the same as the change in enthalpy, that is,

qP = n CP∆T = ∆H

which is also the same in the constant volume CV, we get

qV = n CV∆T

This value is exactly equal to the change in internal energy, that is,

qV = n CV∆T = ∆U

We know that by the molar heat capacity that one mole (n=1) of an ideal gas,

∆H = ∆U + ∆(pV ) = ∆U + ∆(R * T) = ∆U + R * ∆T

Therefore, ∆H = ∆U + R ∆T

By substituting the values of ∆H and ∆U from the above equation, we will get

CP∆T = CV∆T + R ∆T

CP = CV + R

CP – CV = R

At constant pressure CP, we get

qP = n CP∆T

This value is exactly the same as the change in enthalpy, that is,

qP = n CP∆T = ∆H

which is also the same in the constant volume CV, we get

qV = n CV∆T

This value is exactly equal to the change in internal energy, that is,

qV = n CV∆T = ∆U

We know that by the molar heat capacity that one mole (n=1) of an ideal gas,

∆H = ∆U + ∆(pV ) = ∆U + ∆(R * T) = ∆U + R * ∆T

Therefore, ∆H = ∆U + R ∆T

By substituting the values of ∆H and ∆U from the above equation, we will get

CP∆T = CV∆T + R ∆T

CP = CV + R

CP – CV = R

Hence it is proved that the Cp is always greater than the Cv

Cv | Cp |

Cp is the amount of capacity of the heat energy that an element absorbs or release with the change the temperature where a volume change does not happenVolume remains the same, that is, constantAssociated to the internal energy of a system | Cv is the amount of capacity of the heat energy that an element absorbs or release within the change the temperature where a pressure change does not happenPressure remains the same, that is, constantAssociated to the enthalpy of a system |