The objective is to determine the basics understanding of following concepts:

**Law of Conservation of Mass****Law of Conservation of Energy****Co-relation between Mass and Energy****Co-relation between Energy and Work**- Concept about Total Energy
**First Law of Thermodynamics**

## Law of Conservation of Mass

This law states that mass is non destructible or it can not be created or destroyed. According to this law, there exits a relationship for mass flow at different sections in a stream of flow. In the given below fig, flow passing through a pipe is given by:

Steady-state-flow condition for above equation is

Above equation is the result of law of mass conservation and is a one dimensional equation.

### Law of Conservation of Energy

As per this law “energy neither be destroyed nor be created”.

Conversion of energy from ‘one form to another’ took place, whenever system changes its state.

Eaxmples : in applications like:

- Potential energy (PE) changes to Kinetic energy (KE) during flow of water through pipe.
- Automobile K.E changes to heat energy during breaking of automobile on account of friction.
- Conversion of Electrical energy to heat, in the event of current flow through a resistor.

Thus in any process, energy only changes its from and thus will not change the total energy of the system and the surrounding (means universe).

### Relation between Mass and Energy

As per Einstein’s theory of relativity about mass and energy; it is clear that Mass and Energy are convertible.

#### Relation Betweem Energy and Work

Newton’s second law of motion provides the concept of Work, KE and PE.

Assume, if the body moves then its initial and final position and velocity shall be respectively s_{1}, s_{2} and V_{1}, V_{2} because of the involvement of force component F.

From Newton’s second law of motion the magnitude of the force component (F_{s}) is associated with change in magnitude of V by

Above Eq can be re-arranged as

In the above ds/dt is velocity (V) and integrating the equation for initial and final position (s_{1} and s_{2})

Integrating the above equation on both gives

Left-side of the above equation can be equated to

The Quantity

is the Kinetic Energy (KE) of the body and is a scalar quantity and extensive property and change in Kinetic energy is given by

Unit of KE and work are same i.e N-m or J or KJ

Similarly gravitational Potential Energy (PE) of the body is mgh and is a scalar quantity and change in Potential energy is given by

It is a extensive property. Unit of PE is same as that of work i.e N-m or J or KJ.

Where, h is the elevation of the body with respect to earth surface.

Product of force (F) and displacement(ds) is known as work and also be equated to change in Kinetic Energy of the body. Unit is N-m.

Power(P) is rate of transfer of energy by work and can be equated Force(F) X velocity(V).

OR

Rate-of-doing work.

### Total Energy Concept

Total-Energy of the system engulf Kinetic Energy (KE), Potential Energy (PE) and miscellaneous energy. Examples are given as:

- when the spring is compressed. In this case energy is stored within the spring.
- Increase in stored energy is the example of total-energy during battery charging processes.

In above examples the change in system-energy is not on account of changes in kinetic or potential energy but on account of change in internal-energy (U).

When the process changes then its Internal energy is given by U_{2} – U_{1} and specific-internal energy is represented by u expressed on a unit-mass basis.

Total-Energy change is given by:

### Energy Transfer by Heat

So far we have discussed only those interactions between system and surrounding that are related with work. But it is also possible for a closed system to interact with the surrounding that can’t be called as work.

Example : when gas come in contact with the hot surface of a plate in a cylinder, then gas energy increases although no work has performed. This process is called energy transfer by heat.

(Q) is the amount of energy transferred across the boundary of a system. Then Q into a system is considered as positive, while Q out of the system is considered as negative.

Q > 0 (considered as positive) ⇒ Heat transfer to the system

Q < 0 (considered as negative) ⇒ Heat transfer from the system The heat-transfer not just depends on the end-state, but depends on the particular process. Similarly heat also not depends on the end-state.

The value of heat-transfer (Q) depends on the specific process and not just on just end states. The amount of energy transfer by heat in a process is given by integral of:

Where limits means from state 1 to state 2 and do not refer to the values of heat at those states. The sign notation used for heat transfer (Q) is opposite to that of work transfer (W). A Positive value of work (W) implies transfer of energy from system to surroundings and vice versa.

### First Law of Thermodynamics or Energy Balance in a Closed System

Transfer of energy by work (W) or by heat (Q) is the only way by which energy with in the closed system can be changed. The underlying principle is that **Energy is Conserved**.

When energy (heat and work) crosses the boundary in a system, then Internal-energy (U) of the system get change and this phenomenon is called the First Law of Thermodynamics (learn more about engineering thermodynamics)

[Energy Change with in the system during some time interval] = [Net energy transferred in the system boundary by heat transfer process during the same interval] – [Net energy transferred out of the system boundary by work during the same interval]

In the above equation the system energy increases or decreases by an amount equal to the net-energy transferred across the boundary and can be expressed as:

Total Energy (E_{2} – E_{1}) or Δ E | Q – W |

Δ KE + Δ PE + Δ U | Q – W |

Energy balance in differential form (dE) Where dE is property | δQ – δW heat and work are not property |

dE/dt | [δQ /dt – δW/dt] |

In above equation energy transfer across boundary results in change in one or more macroscopic form of energy like KE, PE and Internal energy (U).

Energy balance with respect to time is expressed as:

[Time rate of change of energy contained with in the system at time t] = [Net rate at which energy is being transferred in through heat transfer at time t] – [Net rate at which energy is being transferred out through work at time t]

Since the time rate of change of energy is given by,

Therefore,

dE/dt | [δQ /dt – δW/dt] |

[dKE/dt + dPE/dt + dU/dt] | [δQ /dt – δW/dt] |