Conservation of Energy Formula: Equations & Examples

The conservation of energy formula denotes that energy can neither be created nor destroyed. It can only change from one form of energy to another form. Energy is the capacity to do any work. 

• On Earth, energy is available in multiple forms, ranging from nuclear energy to electrical energy.
• The law of conservation of energy is a very important concept of thermodynamics.
• According to the law of conservation of energy, energy remains uniform throughout the system unless additional energy is added from outside.
• Switching off the light when you leave the room and unplugging appliances when not in use are examples of energy conservation.
• Mathematically, it can be represented as: 

U_T = U_i + W + Q

• Where, U_T denotes the total energy of the system
• U_i represents the initial energy
• W is the work done on or by the system
• Q is the heat added or removed from the system

Key Terms: Law of Conservation of Energy, Conservation of Energy Formula, Energy, Thermodynamics, Solar Energy, Nuclear Energy, Work

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Law of Conservation of Energy

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The law of conservation of energy simply states that energy in all its forms is never created or destroyed completely; it just transforms from one form to another. 

• Every form of energy works on the principle of the law of energy conservation.
• In a system isolated from its surroundings (a closed system), the total energy remains conserved.
• So, in an isolated system such as the universe, if there is a loss of energy in one part, there must be an equal amount of energy gained in another part. 
• Momentum, angular momentum and energy remain conserved in the machines.

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Conservation of Energy Formula

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The amount of energy in any system is determined by the conservation of energy equation. The conservation of energy formula can be represented as – 

U_T = U_i + W + Q

• Where, U_T denotes the total energy of the system
• U_i represents the initial energy
• W is the work done on or by the system
• Q is the heat added or removed from the system
• The change in the internal energy of the system can be determined by:

\(\triangle U = W + Q\)

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Derivation of Conservation of Energy Formula

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There are various forms of energy like tidal energy, heat energy, wave energy, wind energy and solar energy. All these forms of energy are known to transfer from one form to another.

• For instance, in solar panels, the solar energy is transformed into electrical energy using photovoltaic cells.
• Therefore, we can say that the total sum of energy remains constant, however, its subsequent divisions may vary.
• So, mathematically we can represent the law of energy conservation as,

Amount of energy spent in a work = Amount of energy gained in other work

• Now, the derivation of the energy conservation formula is as follows. We can write,

Δ E_sys = E_in − E_out 

• The net amount of energy transferred in or out of any system is mainly seen in the forms of heat (Q), mass (m), or work (W).
• Hence, on rearranging the above equation, we get,

Q − W = E_in − E_out 

• Now, on dividing all the terms by the mass of the system, the equation represents the law of conservation of energy on a unit mass basis, such as

Δ E_sys = Q – W

• Thus, the conservation of energy formula can be written as follows,

\(Q - W = {dE \over dt}\)

Here,

• E_in = Incoming energy
• E_sys = Energy of the system as a whole
• E_out = Outgoing energy
• E = Energy
• Q = Heat
• M = Mass
• W = Work
• T = Time

• The conservation of energy formula can also be written as,

(Initial Kinetic Energy) + (Initial Potential Energy) + (Other Work) = (Final Kinetic Energy) + (Final Potential Energy)

K₁ + U₁ + W_other = K₂ + U₂

Here,

• K₁ = Initial kinetic energy (Joules, J)
• U₁ = Initial potential energy (J)
• W_other = Other work, gained or lost to the system (J)
• K₂ = Final kinetic energy (J)
• U₂ = Final potential energy (J)

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Things to Remember

• Law of energy conservation is applicable to all the forms of energy due to which we can easily harness solar or wind energy for optimum human use.
• The photovoltaic cells help in transforming the solar radiation of the sun into a usable form.
• The Law of energy conservation defines the transfer of energy, whether, kinetic or potential. 
• The conservation of energy formula can be denoted as K₁ + U₁ = K₂ + U₂.
• A loudspeaker is used for the conversion of electrical energy into sound energy 

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