# Energy and Energy Transfer

Prepared by:

Er. Ashok Subedi, Mechanical Engineer, Institute of Engineering (I.O.E)

## Energy and its Meaning

The capacity for performing the work is said to be energy. Alternatively, the ability of system exerting the force at a specific interval is also said to be energy. The magnitude of the force depends on the energy level of the system.

In thermodynamic energy is mainly divided into two groups; i.e. stored energy and transient energy.

## 1. Stored Energy

That energy that is not able to cross the system’s boundary and remains within the system as the intrinsic property is said to be stored energy. It has a distinct value for every state of equilibrium as well as independent of the path, so they are considered as the properties of thermodynamic.

Kinetic energy, potential energy, and internal energy are the stored energy of the system which can be explained as below;

### i) Kinetic energy:

Energy due to the motion of the matter is said to be Kinetic energy with respect to the external reference. It is given as;

KE=(mV^2)/2

where, m=system’s mass and V= system’s velocity

Kinetic energy occurs because of macroscopic phenomena.

### ii) Potential energy:

Energy due to the virtue of the position of the matter is said to be potential energy in the forced field. Along with this energy due to the elastic forces and the surface tension are also considered as the potential energy.

Here in the thermodynamic, mostly potential energy due to the gravitation is used with respect to the certain referral level which is given as;

PE=mgz

where, m= system’s mass, g= acceleration due to gravity and z= system’s elevation. It also occurs because of the macroscopic phenomena.

### iii) Internal Energy

Energy because of the activity of the molecules is said to be internal energy. It can also be defined as the forms of energy in the matter because of the internal structure of the matter which is independent of the external references.

Further, it is the summation of molecular kinetic and potential energy. It occurs due to microscopic phenomena. Internal energy is the function of temperature, i.e. when the temperature increases then the internal energy increases and vice versa.

The specific total energy is defined as the energy of the system per unit mass. If the magnetic, nuclear and electric energy contributions are neglected, then the total energy can be defined as the summation of potential, kinetic and internal energy of the system.

So it can also be said that it is the combination of microscopic and macroscopic phenomena which is given as;

E=KE+PE+U=(mV^2)/2+mgz+U

and

e=E/m=  V^2/2+gz+u

## 2. Transient Energy

That energy which can cross the system’s boundary, i.e. from the system to surrounding and vice versa during the process of thermodynamic is said to be transient energy. It does not possess distinct value at every state of equilibrium because of depending on the properties of both system and surrounding.

In addition, transient energy is path-dependent, so they are not considered as the properties of thermodynamic. Heat and work transfer are examples of transient energy which are explained as below;

### i) Work Transfer:

if the system is displaced or moved by the application of the force in the direction of that applied force, then it is said to be work. Mathematically it can be written as;

But in thermodynamic work is defined as the transient energy which occurs due to the driving forces which acted on the system. Furthermore, the work transfer in a specific thermodynamic process, transfer of energy takes place without the noticeable macroscopic displacement.

Therefore in thermodynamic work transfer is defined as the energy transfer process without involving the mass transfer because of difference in any properties except temperature. Electric potential, pressure are some common properties due to which the work transfer happens in the thermodynamic process.

Different types of notation are used for work transfer like W in kJ, w in kJ/kg, in kW, and W in kW/kg.

Sign convention of the work transfer in thermodynamics:

If the work is performed by the system, then it is taken as positive while if the work is performed on the system, then it is taken as negative.

### ii) Heat Transfer:

the process of transferring the energy without transferring the mass as the function of temperature difference or gradient is called heat transfer. Like work transfer, it is also noted by different notations like Q in kJ, q in kJ/kg, in kW and q in kW/kg.

Sign convention of the heat transfer in thermodynamics:

If the heat is gained by or supplied to the system then it is taken as positive while if the heat is lost by or rejected by the system then it is taken as negative.

## Expression for a Displacement Work Transfer

Let us consider a piston-cylinder arrangement which contains gas. Then the P-V diagram of the system is as given;

Then according to the definition of work transfer;

where, F is the provided force by the pressure of the gas in the cylinder, i.e. F=PA

Putting the value of F in the above equation, the above equation become as;

Since there the pressure of gas displaces the piston, so the volume of the gas expands from V1 to V2. Therefore the above equation can be written as;

This equation indicates that the work transfer can be determined by analyzing the area covered by the P-V diagram.

The work transfer can be determined for several processes of thermodynamic which are explained as below;

### a. Isothermal process:

During this process, the pressure of the ideal gas is inversely proportional to the volume. Mathematically,

The P-V diagram for the isothermal process is as shown.

Considering the initial, final and intermediate states, the above relation can be written as;

P_1  V_1=P_2  V_2= PV

Then pressure at intermediate state is;

P=(P_1  V_1)/V

Then work transfer during the isothermal process can be determined as;

### b. Isobaric Process

During this process, the pressure remains constant, and the P-V diagram for this process is given as;

During this process, the work transfer is provided by the shaded region area in the P-V diagram.

### c. Isochoric process

During this process, there is no displacement of the piston because of which the work transfer is zero. The P-V diagram of the isochoric process is as shown below;

### d. Polytropic process

The process of thermodynamic which follows the relation is said to be a polytropic process where n is said to be the index of polytropic. Further, the above relation is the general relation that varies according to the number of n. if the value of n is equal to γ, then the process is said to be an adiabatic process.

Considering the initial, final and intermediate states, the above relation can be written as;

Then pressure at intermediate state can be determined as;

Then the work transfer is determined as;

Then substituting the value,

P_1 V_1^n=P_2 V_2^n

Now, the above equation becomes as;

This equation is not valid when n=1.

### Power

In general, the rate of doing work is said to be power. But in thermodynamic power is deals with two different modes of energy transfer, i.e. heat transfer and work transfer. In the first case, the rate of heat transfer is said to be thermal power which is the function of the temperature gradient, and mathematically it is given as;

In the second case rate of work, the transfer is said to be mechanical power which is the function of displacement, and mathematically it is given as;