## Law of conservation of energy

**Law of Conservation of energy** or conservation of energy principle in **thermodynamics** states that the total heat or energy of our universe must remain constant. The relation between heat and work in science is the origin of the first law of conservation of energy. The first law of energy conservation in thermodynamics states that energy can neither be created nor be destroyed but may be transferred from one form to another. In other words, when one form of energy disappears, an exact and same amount of other form appears to maintain the net amount of energy in our universe. Hence a definite quantity of electrical energy given to be equivalent quantity of heat or mechanical work.

Conservation of energy in thermodynamics provides the calculation and formula for specific heat change and transfer in cyclic, isothermal, isochoric, and isolated processes in terms of internal energy and work done by the system.

### Energy conservation formula

Let q amount of heat supplied to the system containing one-mole gas in a cylinder fitted with a frictionless weightless moveable piston. At constant pressure, the gas molecules expand from volume V_{1} to V_{2,} and the temperature changes from T_{1} to T_{2}. Therefore, according to the 1st law of thermodynamics, q = dU + w, where dU = change of internal energy. If the work restricted to pressure-volume work or mechanical work then w = PdV. Hence, q = dU + PdV.

Heat change in thermodynamics for ideal and real gases derived from ideal gas law and Van der Waals equation. Therefore, all ideal and real gases obey these energy conservation formulas.

### Change in internal energy formula

#### First law of thermodynamics for cyclic process

Internal energy changes in the cyclic process, dU = 0. Therefore, according to the first law, q = w. Hence from the energy conservation formula in thermodynamics, heat is completely converted into work for the cyclic process.

#### Work done in isothermal process

Internal energy change in the isothermal process for the ideal gas, dU = nc_{v}dT = 0. Therefore, q = w. Hence, thermodynamics heat is completely converted into work for the ideal gas in the isothermal process.

#### Work done in isochoric process

Volume change in isochoric process, dV = 0. From the 1st law of thermodynamics, q = dU = nc_{v}dT. Therefore, heat change to an isochoric process only increases the internal energy or temperature of the system.

#### First law of thermodynamics for isolated system

In an isolated system, neither energy nor matter can be transfer to or from it. Therefore, q = 0 for isolated system. Hence from the energy conservation law of thermodynamics, w = – dU. Therefore, the isolated system uses internal energy for doing work.

### Conservation of energy examples

The net change of the internal energy of the system and surroundings is zero. The change of internal energy independent of the path or way of transformation but heat change and work done dependent on the path of transformation. For example, when the element zinc reacts with copper sulfate in solution, a considerable quantity of heat produced. But if the same redox reaction takes place in the voltaic cell practically no heat evolved and the internal energy converted into electric work.

If oxidation of the mixture of gasoline or burnt gasoline in the air the large quantity of heat produced. But if the same change carried out in the engine, the combustion pushes out the piston and performs work. Here engine produces a Lasser quantity of heat than the oxidizing process. Therefore the magnitude and work done very with the condition of the experiment in thermodynamics energy conservation.