Before reading the text below answer the following question

What do these abbreviations stand for?

1.CGS system

2.SI system

3.TNT

4.BTU

5.RPM

6.°C

7.USS

2.2. You are going to read about the examples of mass–energy equivalence. Six phrases have been removed from the text. Choose from the sentence A – G the one which fits each gap (1 – 6). There is one extra phrase which you don’t need to use.

A after cooling (the heat, light and radiation in this case carried the missing gram of mass)

B However, Einstein’s equations show that all energy has mass.

CWhenever energy is added to a system.

D when testing Einstein’s theory of general relativity.

E and therefore the potential energy, in principle.

F which is sometimes called the "active energy".

G when energy of any kind is added to a resting body.

Practical Examples of Mass–Energy Equivalence

Einstein used the CGS system of units (centimeters, grams, seconds, dynes, and ergs), but the formula is independent of the system of units. In natural units, the speed of light is defined to equal 1, and the formula expresses an identity: E = m. In the SI system (expressing the ratio E / m in joules per kilogram using the value of c in meters per second):

E / m = c2 = (299,792,458 m/s)2 = 89,875,517,870,000,000 J/kg (≈9.0 Ч 1016 joules per kilogram)

So one gram of mass — approximately the mass of a U.S. dollar bill — is equivalent to the following amounts of energy:

89.9 terajoules

24.9 million kilowatt-hours (≈25 GW·h)

21.5 billion kilocalories (≈21 Tcal)

21.5 kilotons of TNT-equivalent energy (≈21 kt)

85.2 billion BTUs

Any time energy is generated, the process can be evaluated from an E = mc2 perspective. For instance, the "Gadget"-style bomb used in the Trinity test and the bombing of Nagasaki had an explosive yield equivalent to 21 kt of TNT. About 1 kg of the approximately 6.15 kg of plutonium in each of these bombs fissioned into lighter elements totaling almost exactly one gram less, 1)_____________. This occurs because nuclear binding energy is released whenever elements with more than 62 nucleons fission.

Another example is hydroelectric generation. The electrical energy produced by Grand Coulee Dam’s turbines every 3.7 hours represents one gram of mass. This mass passes to the electrical devices which are powered by the generators (such as lights in cities), where it appears as a gram of heat and light. Turbine designers look at their equations in terms of pressure, torque, and RPM. 2)____________, and thus the electrical energy produced by a dam's generators, and the heat and light which result from it, all retain their mass, which is equivalent to the energy. The potential energy – and equivalent mass – represented by the waters of the Columbia River as it descends to the Pacific Ocean would be converted to heat due to viscous friction and the turbulence of white water rapids and waterfalls were it not for the dam and its generators. This heat would remain as mass on site at the water, were it not for the equipment which converted some of this potential and kinetic energy into electrical energy, which can be moved from place to place (taking mass with it).

3)_______, the system gains mass. A spring's mass increases whenever it is put into compression or tension. Its added mass arises from the added potential energy stored within it, which is bound in the stretched chemical (electron) bonds linking the atoms within the spring. Raising the temperature of an object (increasing its heat energy) increases its mass. If the temperature of the platinum/iridium "international prototype" of the kilogram—the world’s primary mass standard—is allowed to change by 1°C, its mass will change by 1.5 picograms (1 pg = 1 Ч 10–12 g).

Note that no net mass or energy is really created or lost in any of these scenarios. Mass/energy simply moves from one place to another. These are some examples of the transfer of energy and mass in accordance with the principle of mass–energy conservation.

Note further that in accordance with Einstein’s Strong Equivalence Principle (SEP), all forms of mass and energy produce a gravitational field in the same way. So all radiated and transmitted energy retains its mass. Not only does the matter comprising Earth create gravity, but the gravitational field itself has mass, and that mass contributes to the field too. This effect is accounted for in ultra-precise laser ranging to the Moon as the Earth orbits the Sun 4)________.

According to E=mc2, no closed system (any system treated and observed as a whole) ever loses mass, even when rest mass is converted to energy. This statement is more than an abstraction based on the principle of equivalence, it is a real-world effect.

Potential energy also has mass, but where this mass sits is sometimes difficult to determine. The concept of potential energy is Newtonian, it is defined for the system as a whole. The mass-energy relation together with the law of gravity requires that the potential energy be somewhere, so that its mass can produce a gravitational field. So in relativity, the potential energy always comes from a local field, and it is found wherever the field is varying or has a value which carries energy. Gravitational experiments can locate the field energy, 5)___________.

The one exception is the gravitational field itself. Because the gravitational field can be made to vanish locally by choosing a free-falling frame, it is difficult to locate gravitational energy in an observer independent way. Still, it is possible to define the location of the gravitational energy consistently in several different ways, all of which agree on the total energy. The field energy in the Newtonian limit is the potential energy of a system.

Although all mass, including that in ordinary objects, is energy, this energy is not always in a form which can be used to generate power. All energy, both usable and unusable, has mass, so when people say that certain reactions "convert" mass into "energy", they mean that the mass is converted into specific types of energy, which can be used to do work, 6)______. Practical "conversions" of mass into active energy never make all of the mass into the sort of energy which can be used to do work.

For example, in nuclear fission roughly 0.1% of the mass of fissioned atoms is converted to heat energy and radiation. In turn, the mass of fissioned atoms is only part of the mass of the fissionable material: e.g. in a nuclear fission weapon, the efficiency is 40% at most, meaning that 40% of fissionable atoms actually fission. In nuclear fusion roughly 0.3% of the mass of fused atoms is converted to active energy. In thermonuclear weapons some of the bomb mass is casing and non-reacting components, so the efficiency in converting passive energy to active energy, at 6 kilotons TNT equivalent energy output per kilogram of bomb mass (or 6 megatons per metric ton bomb mass), does not exceed 0.03%.

2.3. Explain the following notions in your own words:

1.generator

2.energy output

3.turbine

4.gravitational field

5.laser ranging

6.chemical bonds

7.free-falling frame