## Conservation of Energy Formula :

Energy spent in one act=Energy gained in the related act

Conservation of Energy Formula is energy transform E_{in} subtraction Energy of out E_{out } is equal to the of any system occurs in the form of energy ΔE_{sys.}Hence the conservation of Energy formula can be written as

E_{in } -E_{out} =ΔE_{sys}

As we know the net amount of energy transfer into or out of any system occurs in the form of heat (Q), mass(m) and work (w).Hence we can rewrite the aforementioned equation as

Conservation of Energy formula is Energy into E_{in }and subtraction Energy out E_{out} is equal to the of any system occurs in the form of heat Q_{(j)} in joule and subtraction work of energy W_{(j)} in joule. Hence the conservation of Energy formula can be written as

E_{in } -E_{out} =Q_{(j)}-W_{(j)}

Upon dividing all the terms into both sides of the equation by the mass of the system, the equation represents the law of conservation of energy on a unit mass basis as shown below

Q-W= Δu

Thus we can write the conservation of energy rate equation as

Q-W =du/dt

## Sample Problems :

## Problem 1:

Calculate the energy conservation of the system? The initial energy and the final energy of a system can be given by 6.450 × 10^{-3} and 3.460 × 10^{-3} respectively.

### Solution :

We can use the following formula to compute the energy conservation of the system.

ΔE_{sys }= E_{in } -E_{out}

ΔE=(6.450 × 10^{-3}) –(3.460 × 10^{-3} )

ΔE= 0.00299× 10^{-3}

## Problem 2:

Calculate the law of conservation of energy? In a particle of charge equal to that of electron and the charge is 1.67× 10^{-27} and mass of the particle is 1.30 × 10^{-27 }kg.

### Solution :

As per the law of conservation of energy formula, we have

Q-W= ΔE_{sys} or

ΔE_{sys} =Q-W

=(1.67 × 10^{-27} )-( 1.30 × 10^{-27 })

=0.37 × 10^{27}