# 7.6 Conservation of energy  (Page 3/10)

 Page 3 / 10

Another example of energy conversion occurs in a solar cell. Sunlight impinging on a solar cell (see [link] ) produces electricity, which in turn can be used to run an electric motor. Energy is converted from the primary source of solar energy into electrical energy and then into mechanical energy.

Energy of various objects and phenomena
Object/phenomenon Energy in joules
Big Bang ${\text{10}}^{\text{68}}$
Energy released in a supernova ${\text{10}}^{\text{44}}$
Fusion of all the hydrogen in Earth’s oceans ${\text{10}}^{\text{34}}$
Annual world energy use $4×{\text{10}}^{\text{20}}$
Large fusion bomb (9 megaton) $3\text{.}8×{\text{10}}^{\text{16}}$
1 kg hydrogen (fusion to helium) $6\text{.}4×{\text{10}}^{\text{14}}$
1 kg uranium (nuclear fission) $8\text{.}0×{\text{10}}^{\text{13}}$
Hiroshima-size fission bomb (10 kiloton) $4\text{.}2×{\text{10}}^{\text{13}}$
90,000-ton aircraft carrier at 30 knots $1\text{.}1×{\text{10}}^{\text{10}}$
1 barrel crude oil $5\text{.}9×{\text{10}}^{9}$
1 ton TNT $4\text{.}2×{\text{10}}^{9}$
1 gallon of gasoline $1\text{.}2×{\text{10}}^{8}$
Daily home electricity use (developed countries) $7×{\text{10}}^{7}$
Daily adult food intake (recommended) $1\text{.}2×{\text{10}}^{7}$
1000-kg car at 90 km/h $3\text{.}1×{\text{10}}^{5}$
1 g fat (9.3 kcal) $3\text{.}9×{\text{10}}^{4}$
ATP hydrolysis reaction $3\text{.}2×{\text{10}}^{4}$
1 g carbohydrate (4.1 kcal) $1\text{.}7×{\text{10}}^{4}$
1 g protein (4.1 kcal) $1\text{.}7×{\text{10}}^{4}$
Tennis ball at 100 km/h $\text{22}$
Mosquito $\left({10}^{–2}\phantom{\rule{0.25em}{0ex}}g at 0.5 m/s\right)$ $1\text{.}3×{\text{10}}^{-6}$
Single electron in a TV tube beam $4\text{.}0×{\text{10}}^{-\text{15}}$
Energy to break one DNA strand ${\text{10}}^{-\text{19}}$

## Efficiency

Even though energy is conserved in an energy conversion process, the output of useful energy or work will be less than the energy input. The efficiency     $\text{Eff}$ of an energy conversion process is defined as

$\text{Efficiency}\left(\text{Eff}\right)=\frac{\text{useful energy or work output}}{\text{total energy input}}=\frac{{W}_{\text{out}}}{{E}_{\text{in}}}\text{.}$

[link] lists some efficiencies of mechanical devices and human activities. In a coal-fired power plant, for example, about 40% of the chemical energy in the coal becomes useful electrical energy. The other 60% transforms into other (perhaps less useful) energy forms, such as thermal energy, which is then released to the environment through combustion gases and cooling towers.

Efficiency of the human body and mechanical devices
Activity/device Efficiency (%) Representative values
Cycling and climbing 20
Swimming, surface 2
Swimming, submerged 4
Shoveling 3
Weightlifting 9
Steam engine 17
Gasoline engine 30
Diesel engine 35
Nuclear power plant 35
Coal power plant 42
Electric motor 98
Compact fluorescent light 20
Gas heater (residential) 90
Solar cell 10

## Phet explorations: masses and springs

A realistic mass and spring laboratory. Hang masses from springs and adjust the spring stiffness and damping. You can even slow time. Transport the lab to different planets. A chart shows the kinetic, potential, and thermal energies for each spring.

## Section summary

• The law of conservation of energy states that the total energy is constant in any process. Energy may change in form or be transferred from one system to another, but the total remains the same.
• When all forms of energy are considered, conservation of energy is written in equation form as ${\text{KE}}_{i}+{\text{PE}}_{i}+{W}_{\text{nc}}+{\text{OE}}_{i}={\text{KE}}_{f}+{\text{PE}}_{f}+{\text{OE}}_{f}$ , where $\text{OE}$ is all other forms of energy besides mechanical energy.
• Commonly encountered forms of energy include electric energy, chemical energy, radiant energy, nuclear energy, and thermal energy.
• Energy is often utilized to do work, but it is not possible to convert all the energy of a system to work.
• The efficiency $\text{Eff}$ of a machine or human is defined to be $\text{Eff}=\frac{{W}_{\text{out}}}{{E}_{\text{in}}}$ , where ${W}_{\text{out}}$ is useful work output and ${E}_{\text{in}}$ is the energy consumed.

## Conceptual questions

Consider the following scenario. A car for which friction is not negligible accelerates from rest down a hill, running out of gasoline after a short distance. The driver lets the car coast farther down the hill, then up and over a small crest. He then coasts down that hill into a gas station, where he brakes to a stop and fills the tank with gasoline. Identify the forms of energy the car has, and how they are changed and transferred in this series of events. (See [link] .)

Describe the energy transfers and transformations for a javelin, starting from the point at which an athlete picks up the javelin and ending when the javelin is stuck into the ground after being thrown.

Do devices with efficiencies of less than one violate the law of conservation of energy? Explain.

List four different forms or types of energy. Give one example of a conversion from each of these forms to another form.

List the energy conversions that occur when riding a bicycle.

## Problems&Exercises

Using values from [link] , how many DNA molecules could be broken by the energy carried by a single electron in the beam of an old-fashioned TV tube? (These electrons were not dangerous in themselves, but they did create dangerous x rays. Later model tube TVs had shielding that absorbed x rays before they escaped and exposed viewers.)

Using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.

Equating ${\text{ΔPE}}_{g}$ and $\text{ΔKE}$ , we obtain $v=\sqrt{2\text{gh}+{{v}_{0}}^{2}}=\sqrt{2\left(\text{9.80 m}{\text{/s}}^{2}\right)\left(\text{20.0 m}\right)+\left(\text{15.0 m/s}{\right)}^{2}}=\text{24.8 m/s}$

If the energy in fusion bombs were used to supply the energy needs of the world, how many of the 9-megaton variety would be needed for a year’s supply of energy (using data from [link] )? This is not as far-fetched as it may sound—there are thousands of nuclear bombs, and their energy can be trapped in underground explosions and converted to electricity, as natural geothermal energy is.

(a) Use of hydrogen fusion to supply energy is a dream that may be realized in the next century. Fusion would be a relatively clean and almost limitless supply of energy, as can be seen from [link] . To illustrate this, calculate how many years the present energy needs of the world could be supplied by one millionth of the oceans’ hydrogen fusion energy. (b) How does this time compare with historically significant events, such as the duration of stable economic systems?

(a) $\text{25}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{years}$

(b) This is much, much longer than human time scales.

#### Questions & Answers

Physics is a physical science that deals with the study of matter in relation to energy
what is physics
a15kg powerexerted by the foresafter 3second
what is displacement
movement in a direction
Jason
hello
Hosea
Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation? can someone please explain this i need it for my final exam
Hi
saeid
hi
Yimam
What is thê principle behind movement of thê taps control
while
Hosea
what is atomic mass
this is the mass of an atom of an element in ratio with the mass of carbon-atom
Chukwuka
show me how to get the accuracies of the values of the resistors for the two circuits i.e for series and parallel sides
Explain why it is difficult to have an ideal machine in real life situations.
tell me
Promise
what's the s . i unit for couple?
Promise
its s.i unit is Nm
Covenant
Force×perpendicular distance N×m=Nm
Oluwakayode
İt iş diffucult to have idêal machine because of FRİCTİON definitely reduce thê efficiency
Oluwakayode
if the classica theory of specific heat is valid,what would be the thermal energy of one kmol of copper at the debye temperature (for copper is 340k)
can i get all formulas of physics
yes
haider
what affects fluid
pressure
Oluwakayode
Dimension for force MLT-2
what is the dimensions of Force?
how do you calculate the 5% uncertainty of 4cm?
4cm/100×5= 0.2cm
haider