Materials Temperatures and Pressures

Gaseous planets consist of gas and fluid to a very great depth in their interiors. At the depth in Jupiter where the pressure is about one bar (~1 atm), there are clouds of frozen ammonia and hydrogen sulfide, which appear brown from the Earth. Below the frozen clouds there is probably a layer of thick fluid clouds (like the clouds on Earth, made of tiny fluid drops instead of ice crystals).Though a commonly chosen pressure for a defined surface is one bar, the average atmospheric pressure at sea level on Earth, on Jupiter, the surface is considered to be below the cloudbanks, at a pressure of 10 bars.

Jupiter's atmosphere can be penetrated by visible and infrared radiation into the troposphere (the deepest part of the atmosphere, where temperature decreases with altitude), down to pressures of a few bars.The upper stratosphere (the layer above the troposphere, where temperature increases with altitude) can also be probed at specific infrared wavelengths that allow the identification of specific ions (for more information, see the

Elements and Isotopes A ll the materials in the solar system are made of atoms or of parts of atoms. A family of atoms that all have the same number of positively charged particles in their nuclei (the center of the atom) is called an element: Oxygen and iron are elements, as are aluminum, helium, carbon, silicon, platinum, gold, hydrogen, and well over 200 others. Every single atom of oxygen has eight positively charged particles, called protons, in its nucleus. The number of protons in an atom's nucleus is called its atomic number: All oxygen atoms have an atomic number of 8, and that is what makes them all oxygen atoms.

Naturally occurring nonradioactive oxygen, however, can have either eight, nine, or 10 uncharged particles, called neutrons, in its nucleus, as well. Different weights of the same element caused by addition of neutrons are called isotopes. The sum of the protons and neutrons in an atom's nucleus is called its mass number. Oxygen can have mass numbers of 16 (eight positively charged particles and eight uncharged particles), 17 (eight protons and nine neutrons), or 18 (eight protons and 10 neutrons). These isotopes are written as 16O, 17O, and 18O. The first, 16O, is by far the most common of the three isotopes of oxygen.

Atoms, regardless of their isotope, combine together to make molecules and compounds. For example, carbon (C) and hydrogen (H) molecules combine to make methane, a common gas constituent of the outer planets. Methane consists of one carbon atom and four hydrogen atoms and is shown symbolically as CH Whenever a subscript is placed by the symbol of an element, it indicates how many of those atoms go into the makeup of that molecule or compound.

Quantities of elements in the various planets and moons, and ratios of isotopes, are important ways to determine whether the planets and moons formed from the same material or different materials. Oxygen again is a good example. If quantities of each of the oxygen isotopes are measured in every rock on Earth and a graph is made of the ratios of 17O/16O versus 18O/16O, the points on the graph will form a line with a certain slope (the slope is 1/2, in fact). The fact that the data forms a line means that the material that formed the Earth was homogeneous; beyond rocks, the oxygen isotopes in every living thing and in the atmosphere also lie on this slope. The materials on the Moon also show this same slope. By measuring oxygen isotopes in many different kinds of solar system materials, it has now been shown that the slope of the plot 17O/16O versus 18O/16O is one-half for every object, but each object's line is offset from the others by some amount. Each solar system object lies along a different parallel line.

At first it was thought that the distribution of oxygen isotopes in the solar system was determined by their mass: The more massive isotopes stayed closer to the huge gravitational force of the Sun, and the lighter isotopes strayed farther out into the solar system. Studies of very primitive meteorites called chondrites, thought to be the most primitive, early material in the solar system, showed to the contrary that they have heterogeneous oxygen isotope ratios, and therefore oxygen isotopes were not evenly spread in the early solar system. Scientists then recognized that temperature also affects oxygen isotopic ratios: At different temperatures, different ratios of oxygen isotopes condense. As material in the early solar system cooled, it is thought that first aluminum oxide condensed, at a temperature of about 2,440°F (1,340°C), and then calcium-titanium oxide (CaTiO ), at a temperature of about 2,300°F (1,260°C), and then a calcium-aluminum-silicon-oxide (Ca2Al2SiO ), at a temperature of about 2,200°F (1,210°C), and so on through other compounds down to iron-nickel alloy at 1,800°F (990°C) and water, at -165°F (-110°C) (this low temperature for the condensation of water is caused by the very low pressure of space). Since oxygen isotopic ratios vary with temperature, each of these oxides would have a slightly different isotopic ratio, even if they came from the same place in the solar system.

The key process that determines the oxygen isotopes available at different points in the early solar system nebula seems to be that simple compounds created with 18O are relatively stable at high temperatures, while those made with the other two isotopes break down more easily and at lower temperatures. Some scientists therefore think that l7O and l8O were concentrated in the middle of the nebular cloud, and l6O was more common at the edge. Despite these details, though, the basic fact remains true: Each solar system body has its own slope on the graph of oxygen isotope ratios.

Most atoms are stable. A carbon-12 atom, for example, remains a carbon-12 atom forever, and an oxygen-16 atom remains an oxygen-16 atom forever, but certain atoms eventually disintegrate into a totally new atom. These atoms are said to be "unstable" or "radioactive." An unstable atom has excess internal energy, with the result that the nucleus can undergo a spontaneous change toward a more stable form. This is called "radioactive decay." Unstable isotopes (radioactive isotopes) are called "radioisotopes." Some elements, such as uranium, have no stable isotopes. The rate at which unstable elements decay is measured as a "half-life," the time it takes for half of the unstable

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Elements and Isotopes (continued) atoms to have decayed. After one half-life, half the unstable atoms remain; after two half-lives, one-quarter remain, and so forth. Half-lives vary from parts of a second to millions of years, depending on the atom being considered. Whenever an isotope decays, it gives off energy, which can heat and also damage the material around it. Decay of radioisotopes is a major source of the internal heat of the Earth today: The heat generated by accreting the Earth out of smaller bodies and the heat generated by the giant impactor that formed the Moon have long since conducted away into space.

sidebar "Elements and Isotopes" on page 20). Direct information about deeper layers of Jupiter has also been made available by the Galileo probe, which penetrated Jupiter to a pressure of about 20 bars. This probe entered a clear zone, thought to be dry and hot compared to the cloudy belts of the planet, and so its data may not be representative of the entire atmosphere.

In these ways compositions and temperatures of the atmosphere to depths corresponding to a few bars in pressure have been directly measured. At greater depths, the internal structures of Jupiter are only known from indirect measurements and theoretical modeling.

Jupiter is thought to consist primarily of primordial gases from the protoplanetary disk, mostly hydrogen and helium. Its central core is probably rock and ice with a mass of about 10 to 30 Earth masses.The entire cloud zone that is seen in images of Jupiter is extremely thin, only about 31 miles (50 km), and below it lies a clear atmosphere mainly of gaseous helium and hydrogen. As pressures increase inside the planet with depth, the helium and hydrogen gradually become liquid (see figure on page 23).

Pressures inside the planet finally become high enough to press the hydrogen into a metallic solid in which electrons move freely among the hydrogen nuclei (this assertion is based on modeling and experimentation, not on direct observations). This abrupt transition to hydrogen and helium metal occurs at about 0.78 of the radius of the planet. The hydrogen metal phase is not hard and stiff, as metal is on Earth's surface. This substance is hot, though solid, and moves in currents like a thick liquid (for more, see the sidebar "Rheology, or Why Solids Can Flow" on page 92). The last compositional layer in Jupiter is thought to be an ice-silicate core, taking up only the inner 20 percent of the planet's radius.

While pressures are low enough to allow the hydrogen and helium to be gases or liquids, they freely intermix. When pressures increase (see the sidebar "What Is Pressure?" on page 24) to the point that hydrogen is pressed into a metallic solid; however, helium cannot fit into the hydrogen metal structure, and separates into distinct droplets. The helium droplets are heavier than the hydrogen metal, and so they sink further into Jupiter's interior, as a sort of helium rain. This sinking releases energy that reheats the interior. As less dense helium gas transforms to liquid and liquid to dense metal beneath the hydrogen layer, the planet becomes denser without changing its mass. This transformation may contribute to the tiny, ongoing contraction of the planet. The helium rain is a hypothesis arrived at from theory, since it cannot be observed directly.The descent of helium into the deep planet, however,

Internal Structure of Jupiter

Cloud layer; about 30 miles (50 km) chick Gaseous and liquid hydrogen and helium

Metallic hydrogen and helium Rock and ice core

78 percent of radius: depth of 9700 miles (15.600 km) 200 GPa pressure 18,000°F (10,000°C)

20 percent of radius: depth of 35500 miles (56,900 km) 4500 GPa pressure 36,000°F (20,000°C)

44,424 miles (71,492 km)

The internal structure of Jupiter beneath the cloud layer is described using theory, as there are no direct measurements.

Internal Structure of Jupiter

What Is Pressure? The simple definition of pressure (p) is that it is force (F) per area (a):

Atmospheric pressure is the most familiar kind of pressure and will be discussed below. Pressure, though, is something felt and witnessed all the time, whenever there is a force being exerted on something. For example, the pressure that a woman's high heel exerts on the foot of a person she stands on is a force (her body being pulled down by Earth's gravity) over an area (the area of the bottom of her heel). The pressure exerted by her heel can be estimated by calculating the force she is exerting with her body in Earth's gravity (which is her weight, here guessed at 130 pounds, or 59 kg, times Earth's gravitational acceleration, 32 ft/sec2, or 9.8 m/sec2) and dividing by the area of the bottom of the high heel (here estimated as one square centimeter):

The resulting unit, kg/ms2, is the same as N/m and is also known as the pascal (Pa), the standard unit of pressure (see appendix 1, "Units and Measurements," to understand more). Although here pressure is calculated in terms of pascals, many scientists refer to pressure in terms of a unit called the atmosphere. This is a sensible unit because one atmosphere is approximately the pressure felt from Earth's atmosphere at sea level, though of course weather patterns cause continuous fluctuation. (This fluctuation is why weather forecasters say "the barometer is falling" or "the barometer is rising:" The measurement of air pressure in that particular place is changing in response to moving masses of air, and these changes help indicate the weather that is to come.) There are about 100,000 pascals in an atmosphere, so the pressure of the woman's high heel is about the same as 57.8 times atmospheric pressure.

What is atmospheric pressure, and what causes it? Atmospheric pressure is the force the atmosphere exerts by being pulled down toward the planet by the planet's gravity, per unit area. As creatures of the Earth's surface, human beings do not notice the pressure of the atmosphere until it changes; for example, when a person's ears pop during a plane ride because the atmospheric pressure lessens with altitude. The atmosphere is thickest (densest) at the planet's surface and gradually becomes thinner (less and less dense) with height above the planet's surface. There is no clear break between the atmosphere and space: the atmosphere just gets thinner and thinner and less and less detectable. Therefore, atmospheric pressure is greatest at the planet's surface and becomes less and less as the height above the planet increases. When the decreasing density of the atmosphere and gravity are taken into consideration, it turns out that atmospheric pressure decreases exponentially with altitude according to the following equation:

o where g is the gravitational acceleration of that planet, and p is the density of the atmosphere at the planet's surface.

Just as pressure diminishes in the atmosphere from the surface of a planet up into space, pressure inside the planet increases with depth. Pressure inside a planet can be approximated simply as the product of the weight of the column of solid material above the point in question and the gravitational acceleration of the planet. In other words, the pressure P an observer would feel if he or she were inside the planet is caused by the weight of the material over the observer's head (approximated as ph, with h the depth you are beneath the surface and p the density of the material between the observer and the surface) being pulled toward the center of the planet by its gravity g:

The deeper into the planet, the higher the pressure.

should produce a lack of helium at the surface in comparison to solar values. This prediction is in fact observed at the surface: Galileo observed a reduction in helium in the surface of Jupiter, compared to expected solar system values. There is also a deficit in neon, perhaps because neon can dissolve into the helium droplet and be carried into the deep interior as well.

At Jupiter's surface the radius at which pressure is about 10 bars (10-3 GPa), the temperature is -148°F (-100°C). Between the surface and just 22 percent of the way down into the planet, where the molecular hydrogen and helium become metallic, the temperature has risen to 18,000°F (10,000°C), and the pressure to 1,974,000 atm (200 GPa), 105 times the 10 bar surface pressure. At the boundary of Jupiter's core, 80 percent of the way to the planet's center, temperatures are thought to reach 36,000°F (20,000°C).

When smaller bodies, often called planetesimals, are colliding and sticking together, creating a single larger body (perhaps a planet), they are said to be accreting. Eventually the larger body may even have enough gravity itself to begin altering the paths of passing planetesimals and attracting them to it. In any case, the process of accretion adds tremendous heat to the body, by the transformation of the kinetic energy of the planetesimals into heat in the larger body. Models of the accretion of Jupiter indicate that its original core temperature may have been as high as 180,000°F (100,000°C).To understand kinetic energy, start with momentum, p, which is defined as the product of a body's mass m and its velocity v:

Sir Isaac Newton called momentum "quality of movement." The greater the mass of the object, the greater its momentum, and likewise, the greater its velocity, the greater its momentum.A change in momentum creates a force, such as a person feels when something bumps into her. The object that bumps into her experiences a change in momentum because it has suddenly slowed down, and what she experiences is a force.The reason she feels more force when someone tosses a full soda to her than when they toss an empty soda can to her is that the full can has a greater mass, and therefore momentum, than the empty can, and when it hits her it loses all its momentum, transferring to her a greater force.

How does this relate to heating by accretion? Those incoming plan-etesimals have momentum due to their mass and velocity, and when they crash into the larger body, their momentum is converted into energy, in this case, heat.The energy of the body, created by its mass and velocity, is called its kinetic energy. Kinetic energy is the total effect of changing momentum of a body, in this case, as its velocity slows down to zero. Kinetic energy is expressed in terms of mass m and velocity v:

Students of calculus might note that kinetic energy is the integral of momentum with respect to velocity:

The kinetic energy is converted from mass and velocity into heat energy when it strikes the growing body. This energy, and therefore heat, is considerable.The huge heat of accretion has been slowly radiating out of the planet ever since. Jupiter still produces twice the heat that it receives from the Sun; therefore Jupiter's energy budget is not dominated by the Sun, as Earth's energy budget is. In fact, Jupiter was probably so hot from the heat of accretion when it first formed that it would have glowed in visible light, like a red-hot piece of metal does, and radiated so much heat that it blew the atmospheric gases away from its moons.

The center of the core of Jupiter is thought to be about 41,400°F (23,000°C). Measurements of heat flow at Jupiter's surface have been made from both ground-based observations and from Voyager, and the heat flowing through Jupiter's surface now supports a core temperature of about this magnitude.Though this means that the core has lost three-quarters of its heat of accretion, it is still hotter than the surface of the Sun. The core is thought to be a solid nucleus of only about 3 percent of Jupiter's mass, with a pressure estimated to be between 30,000,000 to 45,000,000 atm (3,000 and 4,500 GPa).The pressure at the center of the Earth is only about 3,553,200 atm (360 GPa), even though Earth is made of much denser material.

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