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# Joule's Mechanical Equivalent of Heat: A Conversion Factor

### Key Takeaways

• In the classical experiment by James Joule, the potential energy of two falling masses was converted to heat energy.

• Joule’s mechanical equivalent of heat is the amount of work required to produce 1 calorie of heat.

• According to the first law of thermodynamics, the change in internal energy associated with a system is equal to the sum of work done by the system and heat added to the system. The first experiment to test the equivalence of motion and heat energy was conducted in the 19th century by James Joule

Consider a steam turbine; the heat energy generated by the steam is supplied to the turbine to produce mechanical motion. In this example, the heat energy is converted into mechanical energy. Generally, in certain systems, work and heat energy can be mutually interchangeable. The energy supplied in one form (either heat energy or mechanical energy) to a system can deliver outcomes in another form. Joule’s mechanical equivalent of heat enables the mutual conversion of mechanical energy and heat energy.

Time for a History Lesson

### Joule’s Experiment

The first experiment to test the equivalence of motion and heat energy was conducted in the 19th century by James Joule. In this classical experiment, the potential energy of two falling masses was converted to heat energy.

The experimental setup consisted of two masses attached to a paddle wheel through a rope. The paddle wheel led to a container of water. When the two masses were moved, there was a loss in potential energy and the paddle wheel rotated with the movement of masses. The turning of the paddle wheel increased the friction between the wheel and the water.

The rise in temperature of the water was observed as the rise in internal energy of water, which was due to the movement of the masses. It was summarized as the conversion of potential energy to heat energy. The work done by masses produced a rise in the temperature of the water. Through this experiment, Joule proved the effect of mechanical work in producing heat energy.

## The Mechanical Equivalent of Heat

The conversion of mechanical energy to heat energy and vice versa brings the concept of the mechanical equivalent of heat–the internal energy associated with a system can be altered either by doing work to the system or by adding heat to the system. This is the fundamental concept of thermodynamic systems. Applications such as power plants, refrigerators, and engines utilize the possibility of heat-to-work conversion and vice versa to achieve their intended outcomes.

From Joule’s experiment, it was discovered that 4.186 Joules of energy is required to raise the temperature of a 1g object by 1°C. This correlation between heat energy and work establishes the fundamental concept of Joule’s mechanical equivalent of heat, which basically describes the amount of work that is required to produce 1 calorie of heat.

Joule’s mechanical equivalent of heat can be mathematically represented as follows: As Joule’s mechanical equivalent of heat facilitates conversion from one system of units to another, it is just a dimensionless quantity. ## Establishing the Science of Thermodynamics

Thermodynamics is a well-established branch of science that deals with the relationship between work, temperature, energy, and heat. The concept of Joule’s mechanical equivalent of heat played a significant role in establishing thermodynamics as an advanced branch of science. The equivalency between the work and heat energy led to the formulation of the first law of thermodynamics.

### First Law of Thermodynamics

According to the first law of thermodynamics, the change in internal energy associated with a system is equal to the sum of work done by the system and the heat added to the system. A state at which a system exists can be due to the input of work, the input of heat, or a combination of both.

## Electrical Energy Conversion to Heat

Joule’s mechanical equivalent of heat and the electrical equivalent of heat can both be determined using mathematical equations. Imagine an electrical coil immersed in water. Current is flowing through the element. As time lapses, the water heats up due to the dissipation of electrical energy into the water in the form of heat energy.

The electrical energy dissipated in the form of heat can be given by the equation: The unit Watt second is equivalent to 1 Joule. The commonly used unit of electrical energy kWhr can be equated as: ## Determine the Mechanical Equivalent of Heat With PCB Tools

Cadence’s suite of PCB design and analysis tools can assist you in determining the heat energy to mechanical energy equivalent and vice versa. Cadence offers advanced design tools that ensure the development of efficient electro-mechanical systems incorporating multiple energy conversions.

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