Calculating temperature: escape velocity of helium atoms

To escape Earth’s gravity, an object near the top of the atmosphere (at an altitude of 100 km) must travel away from Earth at 11.1 km/s. This speed is called the
escape velocity . At what temperature would helium atoms have an rms speed equal to the escape velocity?

Strategy

Identify the knowns and unknowns and determine which equations to use to solve the problem.

Solution

Identify the knowns:
v is the escape velocity, 11.1 km/s.

Identify the unknowns: We need to solve for temperature,
T . We also need to solve for the mass
m of the helium atom.

Determine which equations are needed.

To get the mass
m of the helium atom, we can use information from the periodic table:

This temperature is much higher than atmospheric temperature, which is approximately 250 K
$(\mathrm{-25}\phantom{\rule{0.2em}{0ex}}\text{\xb0}\text{C or}\phantom{\rule{0.2em}{0ex}}-10\phantom{\rule{0.2em}{0ex}}\text{\xb0}\text{F})$ at high elevation. Very few helium atoms are left in the atmosphere, but many were present when the atmosphere was formed, and more are always being created by radioactive decay (see the chapter on nuclear physics). The reason for the loss of helium atoms is that a small number of helium atoms have speeds higher than Earth’s escape velocity even at normal temperatures. The speed of a helium atom changes from one collision to the next, so that at any instant, there is a small but nonzero chance that the atom’s speed is greater than the escape velocity. The chance is high enough that over the lifetime of Earth, almost all the helium atoms that have been in the atmosphere have reached escape velocity at high altitudes and escaped from Earth’s gravitational pull. Heavier molecules, such as oxygen, nitrogen, and water, have smaller rms speeds, and so it is much less likely that any of them will have speeds greater than the escape velocity. In fact, the likelihood is so small that billions of years are required to lose significant amounts of heavier molecules from the atmosphere.
[link] shows the effect of a lack of an atmosphere on the Moon. Because the gravitational pull of the Moon is much weaker, it has lost almost its entire atmosphere. The atmospheres of Earth and other bodies are compared in this chapter’s exercises.

it means that the total charge of a body will always be the integral multiples of basic unit charge ( e )
q = ne
n : no of electrons or protons
e : basic unit charge
1e = 1.602×10^-19

Riya

is the time quantized ? how ?

Mehmet

What do you meanby the statement,"Is the time quantized"

Mayowa

Can you give an explanation.

Mayowa

there are some comment on the time -quantized..

Mehmet

time is integer of the planck time, discrete..

Mehmet

planck time is travel in planck lenght of light..

Mehmet

it's says that charges does not occur in continuous form rather they are integral multiple of the elementary charge of an electron.

Tamoghna

it is just like bohr's theory.
Which was angular momentum of electron is intral multiple of h/2π

The properties of a system during a reversible constant pressure non-flow process at P= 1.6bar, changes from constant volume of 0.3m³/kg at 20°C to a volume of 0.55m³/kg at 260°C. its constant pressure process is 3.205KJ/kg°C
Determine: 1. Heat added, Work done, Change in Internal Energy and Change in Enthalpy

this is the energy dissipated(usually in the form of heat energy) in conductors such as wires and coils due to the flow of current against the resistance of the material used in winding the coil.

Henry

it is the work done in moving a charge to a point from infinity against electric field

As w=mg where m is mass and g is gravitational force... Now if we consider the earth is in gravitational pull of sun we have to use the value of "g" of sun, so we can find the weight of eaeth in sun with reference to sun...

Prince

g is not gravitacional forcé, is acceleration of gravity of earth and is assumed constante. the "sun g" can not be constant and you should use Newton gravity forcé. by the way its not the "weight" the physical quantity that matters, is the mass

Jorge

Yeah got it... Earth and moon have specific value of g... But in case of sun ☀ it is just a huge sphere of gas...

Prince

Thats why it can't have a constant value of g
....

Prince

not true. you must know Newton gravity Law . even a cloud of gas it has mass thats al matters. and the distsnce from the center of mass of the cloud and the center of the mass of the earth

Jorge

please why is the first law of thermodynamics greater than the second

every law is important, but first law is conservation of energy, this state is the basic in physics, in this case first law is more important than other laws..

Mehmet

First Law describes o energy is changed from one form to another but not destroyed, but that second Law talk about entropy of a system increasing gradually

Mayowa

first law describes not destroyer energy to changed the form, but second law describes the fluid drection that is entropy. in this case first law is more basic accorging to me...

Mehmet

define electric image.obtain expression for electric intensity at any point on earthed conducting infinite plane due to a point charge Q placed at a distance D from it.