# Internal Energy

## What is called Internal Energy?

Random motions of small particles of a system such as atoms or molecules may have translation, rotary or vibration motion within the mass of system. These moving particles posses kinetic energy called internal energy of the system.

All substances are made up of small particles such as atoms and molecules. These particles remain in the state of continuous random motion in the mass of substance.

Heat is a part of this internal energy which can be transferred from one body to another body due to temperature difference between them. Once heat is transferred from first body to second body, it becomes a part of internal energy in the second body.

Therefore, heat is defined as the energy in transit that flows from one body to another body due to temperature difference between them.

Hence, internal energy is purely a form of kinetic energy of molecules. Internal energy is also called energy in transit.

### Change in Internal Energy

Change in internal energy of a thermodynamic system is a function of its temperature.

Consider that a system undergoes a thermodynamic process in which ( \Delta Q ) is the total quantity of heat added to the system.

Then according to the first law of thermodynamics, we have got the relation –

\Delta Q = ( \Delta U + \Delta W )

This quantity of heat energy added to the system will be used to perform two tasks.

1. To increase the temperature of the system by increase in internal energy i.e. ( \Delta U ) .
2. To do some work i.e. ( \Delta W ) .

Therefore, change in internal energy of the system will be –

\Delta U = ( \Delta Q - \Delta W )

When, heat is added to a system at constant volume, then work done by the system will be zero.

\Delta W = P \times \Delta V = P \times 0 = 0

Therefore, \quad \Delta U = ( \Delta Q - 0 ) = \Delta Q

Hence, change in internal energy of a system is expressed as quantity of heat added at constant volume.

Therefore, \quad \text {Change in internal energy of a system } = \text {Heat added at constant volume to the system}

Or, \quad \Delta U = n \ C_v \Delta T

### Internal Energy is a State Function

Expression for change in internal energy i.e. [ \Delta U = n \ C_v \Delta T ] is applicable for an ideal gas undergoing any thermodynamic process irrespective of change in pressure or volume.

Thus, internal energy of a system only depends upon the temperature of the system. So, internal energy of a system is a state function.

### Heat and Internal Energy

1. Heat ( Q ) , work ( W ) and internal energy ( U ) , all are the forms of transferable energy which can be transferred from one system to another system or from one body to another body.
2. Heat and work are path functions which depend upon the real path followed by the process. But internal energy is a state function which depend upon temperature of the system.
3. Heat energy transfer takes place due to difference between the temperature of system and surrounding.
4. Work energy transfer takes place due to change in position of a flexible boundary such as piston cylinder arrangement which is called expansion or compression.
5. Change in internal energy takes place due to change in temperature of the system.

## Heat

Heat is a form of energy which produces the sensation of hotness or coldness of a body in comparison to other body.

### Units of Heat

The CGS unit of heat is calorie. One calorie is defined as the heat energy required in raising the temperature of one gram of water through ( 1 \degree C ) .

The SI unit of heat is joule. Numerical value of 1 calorie is –

1 \ \text {calorie} = 4.186 \ \text {joule}

### Mechanical Equivalent of Heat

Work and heat both are the forms of energy. Work is mechanical energy and heat is thermal energy.

By experiments, Joule establishes a relation between work done and heat produced.

Joule stated that

When a given amount of work ( W ) energy is converted into heat energy, always the equal quantity of heat energy ( Q ) is produced.

Or, \quad W = J Q

Or, \quad J = \left ( \frac {W}{Q} \right )

• The proportionality constant J is called Joule’s mechanical equivalent of heat.

Thus, Joule’s mechanical equivalent of heat can be defined as the amount of work that require to produce unit quantity of heat.

Also we know that ( 1 ) calorie of heat is equivalent to ( 4.186 ) Joule of work. This means that ( 1 ) calorie of heat can be produced by using ( 4.186 ) Joule of work.

Therefore, Joule’s mechanical equivalent of heat is given by –

J = 4.186 \ J \ \text {cal}^{- 1}

Or, \quad J = 4.186 \times 10 ^ 7 \text {erg-cal}^{ - 1 }

## Temperature ( Degree of internal energy )

Temperature is the degree of hotness or coldness of a body.

• It is the measure of internal energy of a system.
• Heat always flow from a body at high temperature to a body at low temperature.

Thus, temperature can be defined as the thermal state of a body which decides the direction of flow of heat energy by comparing the thermal state of another body when placed in thermal contact to each other.

### Heat versus Temperature

 Sl. No. Heat Temperature 1 Heat is a form of energy which produces the sensation of hotness or coldness. Temperature is the degree of hotness or coldness of the body. 2 It is a cause. When some heat is supplied to a body its temperature increases. It is the effect. It tells that heat is added or removed from body. 3 Heat flows from high temperature to low temperature irrespective of the quantity of heat possessed by bodies in contact. Temperature decides the direction of flow of heat. 4 It is measured in cal, kilo-cal or joule. It is measured in Celsius, Fahrenheit or Kelvin.

## Heat Transfer

Heat transfer is the process which involves transfer of energy in transit from one body to another due to temperature difference called temperature gradient.

The rate of change of temperature with respect to the distance in the direction of heat flow is known as temperature gradient.

Therefore, temperature gradient is the reason which causes conduction of heat. It is expressed as \left ( \frac { \delta t }{ L } \right )

Let, ( T_1 ) and ( T_2 ) are the temperatures of two isothermal surfaces of a body. Let, the surfaces are separated by a distance ( L ) .

Then temperature gradient between these surfaces will be –

\left ( \frac { \delta t }{ L } \right ) = \left ( \frac {T_1 - T_2}{L} \right ) .

## Modes of Heat Transfer

An instructor, distributing question paper to the students in a class room may follow the following techniques –

1. The teacher could deliver the paper to a student nearest to him who delivers the same to the next student and so on till finally it reaches the last student.
2. The teacher could carry the paper himself to each student and to the last student.
3. The teacher could throw the question paper so that it reaches the last student.

The transport of heat energy from one region to another occurs in similar manners stated above. The question paper corresponds to heat energy and the students correspond to the molecules of the substance.

These three modes of heat transport which are very similar to the methods of distribution of papers to students are termed as –

1. Conduction.
2. Convection and

### Conduction

Conduction is the process of heat transfer in which heat is transmitted from one region to another region through molecular collisions without any actual flow of matter.

• Heat transfer takes place as a result of transfer of internal energy from one molecule to nearby molecules.
• Heat transfer in solids takes place by conduction.

### Convection

Convection is a process of heat transfer from high temperature region to the lower temperature region by the actual movement of the material particles.

• Convection occurs in liquids and gases.
• Since molecules are free to move within the mass of substance, they carry the energy from one region to another.