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Thermodynamics: Energy Transferred by Work

Energy Transferred by Work

Similar to heat energy, energy due to work is measured by the energy the crosses the boundaries of the system. So if you know that that there is energy crossing the boundaries of the system, and it is not heat, then that means it must be work.

So what exactly is work? Work is the energy transferred as a force acts through a certain distance. This can be simply defined as the equation below.

Work done by a force and distance Equation (1)

F = Force

s = distance traveled


Energy of a particle length time unit force

Equation 1 is the simplest equation to express mechanical work. However, there are more specific equations that can represent work. For example the work of a rotating shaft that is rotating at a constant speed is expressed by equation 2.

Rotary Work Equation (2)

n = number of rotations

T = Torque


In equation 2, n represents the number of revolutions, while T represents the torque applied to the shaft to cause it to rotate. Next, you can modify equation 2 to find the power required to rotate the shaft; refer to equation 3.

Rotatry Power Equation (3)

ω = Angular Velocity


In equation 4, ω represents that angular velocity of the shaft as it rotates. Now if you compare equation 3 to equation 2 you should notice that equation 3 is simply work over a unit time. This means if you want to know how much power is required to do a certain amount of work in a specific amount of time all you would have to do is divide work by time to obtain the required power.

You can also calculate the required work to compress or stretch a spring by using the following equation.

Spring Work Equation (4)

k = Spring constant


Spring energy

Equation 4 can also be applied to solid shafts that are under a normal force once you calculate that shafts stiffness. To learn more about how to calculate the stiffness of a shaft refer to the strength of materials section.

Finally, a change in energy due to work can be related to lifting a body up a certain height; refer to equation 5.

Potential Energy Equation (5)

m = mass

g = gravitational constant

z = height


Spring energy

From equation 2-5 you may have noticed that these equations represent a potential or a kinetic energy equation. So from that, if you can calculate the potential or kinetic energy due to some mechanical change, then you can effectively calculate the change in energy due to mechanical work.

In addition to mechanical work, you can change a systems total energy through electrical work. To do this you multiply electrical power by some unit time; refer to equation 7. Equation 6 represents electrical power.

Electrical Power Equation (6)

V = Volatage

I = Curent


Electrical Work Equation (7)

t = time


From equations 6 and 7, V represents the electrical voltage and I represents the electrical current.

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