Video Transcript
Which of the following correctly
represents the energy dissipated, 𝐸 sub D, in an energy conversion process
between energy category A, 𝐸 sub A, and energy category B, 𝐸 sub B? (A) 𝐸 sub D equals the absolute
value of Δ𝐸 sub A plus Δ𝐸 sub B. (B) 𝐸 sub D equals the absolute
value of Δ𝐸 sub A over the absolute value of Δ𝐸 sub B. (C) 𝐸 sub D equals the absolute
value of Δ𝐸 sub A minus Δ𝐸 sub B. (D) 𝐸 sub D equals the absolute
value of Δ𝐸 sub B over the absolute value of Δ𝐸 sub A.
In this question, we’re asked to
choose the option that correctly represents the energy dissipated, 𝐸 sub D, in
an energy conversion process between energy category A, 𝐸 sub A, and energy
category B, 𝐸 sub B. In order to figure this out, we
will need to remember some information about energy conversion and what
dissipated energy is.
Energy conversion refers to
energy being converted from one category to another, gravitational potential
energy to kinetic energy for an example. We know that from the
conservation of energy, energy cannot be created or destroyed. It will just be converted from
one form to another. When energy is converted from
one category to another, some of it can be lost to its environment, by heat, for
example. This is what we call dissipated
energy. It is energy that leaves the
system during energy conversion and is lost to the environment. We can describe this process
using the formula the amount of energy lost as category one is equal to the
amount of energy converted to category two plus the amount of energy
dissipated.
So let’s take the formula and
plug in the variables given in the problem. The energy lost from category A
will be equal to the energy gained by category B plus the energy lost to
dissipation, 𝐸 sub D. We can represent the change in
energy with a Δ symbol. So we can write this as Δ𝐸 sub
A equals Δ𝐸 sub B plus 𝐸 sub D. We can make the energy
dissipated, 𝐸 sub D, the subject by subtracting both sides of the equation by
Δ𝐸 sub B. Doing this, we learn that the
energy dissipated, 𝐸 sub D, is equal to Δ𝐸 sub A minus Δ𝐸 sub B.
A negative amount of energy
makes no sense. So we need to take the absolute
value of the right-hand side. Therefore, the equation we are
looking for is 𝐸 sub D is equal to the absolute value of Δ𝐸 sub A minus Δ𝐸
sub B. This corresponds with option
(C). So this looks like the correct
answer. But to be certain, let’s check
the other answer options.
Option (A) suggests the energy
dissipated is equal to the total energy of energy category A and energy category
B. But this is not the definition
of dissipated energy, so option (A) is incorrect. Options (B) and (D) suggest that
the energy dissipated is a ratio of the two energy categories, which again is
not the definition of dissipated energy. So these options must be
incorrect too. This means that option (C), 𝐸
sub D equals the absolute value of Δ𝐸 sub A minus Δ𝐸 sub B, must be the
correct answer.
