### Energy and Power Equivalences - Thermodynamic Properties

**Thermodynamics Directory**** | Heat Transfer Directory**

*Energy and power Equivalences *

The various forms of energy involved in energy transfer systems (such as potential energy, kinetic energy, internal energy, P-V energy, work and heat) may be measured in numerous basic units. In general, three types of units are used to measure energy: (1) mechanical units, such as the foot-pound-force (ft-lbf); (2) thermal units, such as the British thermal unit (Btu); and (3) electrical units, such as the watt-second (W-sec). In the mks and cgs systems, the mechanical units of energy are the joule (j) and the erg, the thermal units are the kilocalorie (kcal) and the calorie (cal), and the electrical units are the watt-second (W-sec) and the erg. Although the units of the various forms of energy are different, they are equivalent.

Some of the most important experiments in science were those conducted by J. P. Joule in 1843, who showed quantitatively that there was a direct correspondence between mechanical and thermal energy. These experiments showed that one kilocalorie equals 4,186 joules. These same experiments, when performed using English system units, show that one British thermal unit (Btu) equals 778.3 ft-lbf. These experiments established the equivalence of mechanical and thermal energy. Other experiments established the equivalence of electrical energy with both mechanical and thermal energy. For engineering applications, these equivalences are expressed by the following relationships.

1 ft-lbf = 1.286 x 10^{-3 }Btu = 3.766 x 10^{-7 }kW-hr

1 Btu = 778.3 ft-lbf = 2.928 x 10^{-4 }kW-hr

1 kW-hr = 3.413 x 10^{3 }Btu = 2.655 x 10^{6 }ft-lbf

There is one additional unit of energy encountered in engineering applications. It is the horsepower-hour (hp-hr). It is a mechanical unit of energy defined by the following relationship:

1 hp-hr = 1.980 x 10^{6 }ft-lbf

These relationships can be used to convert between the various English system units for the various forms of energy.

Most computations involving the energy of the working fluid in an energy transfer system are performed in Btu’s. Forms of mechanical energy (such as potential energy, kinetic energy, and mechanical work) and other forms of energy (such as P-V energy) are usually given in foot-pounds-force. These are converted to Btu’s by using 1 Btu = 778.3 ft-lbf.

This conversion factor is often used. In fact, a constant called the mechanical equivalent of heat, usually denoted by the symbol J and sometimes referred to as *Joule’s constant*, is defined as:

*Power *is defined as the time rate of doing work. It is equivalent to the rate of the energy transfer. Power has units of energy per unit time. As with energy, power may be measured in numerous basic units, but the units are equivalent. In the English system, the mechanical units of power are foot-pounds-force per second or per hour (ft-lbf/sec or ft-lbf/hr) and horsepower (hp). The thermal units of power are British thermal units per hour (Btu/hr), and the electrical units of power are watts (W) or kilowatts (kW). For engineering applications, the equivalence of these units is expressed by the following relationships.

1 ft-lbf/sec = 4.6263 Btu/hr = 1.356 x 10^{-3 }kW

1 Btu/hr = 0.2162 ft-lbf/sec = 2.931 x 10^{-4 }kW

1 kW = 3.413 x 10^{3 }Btu/hr = 737.6 ft-lbf/sec

Horsepower is related to foot-pounds-force per second (ft-lbf/sec) by the following relationship:

1 hp = 550.0 ft-lbf/sec

These relationships can be used to convert the English system units for power.