# 2.2 Pressure, temperature, and rms speed  (Page 9/18)

 Page 9 / 18

Statistical mechanics says that in a gas maintained at a constant temperature through thermal contact with a bigger system (a “reservoir”) at that temperature, the fluctuations in internal energy are typically a fraction $1\text{/}\sqrt{N}$ of the internal energy. As a fraction of the total internal energy of a mole of gas, how big are the fluctuations in the internal energy? Are we justified in ignoring them?

Which is more dangerous, a closet where tanks of nitrogen are stored, or one where tanks of carbon dioxide are stored?

One where nitrogen is stored, as excess ${\text{CO}}_{2}$ will cause a feeling of suffocating, but excess nitrogen and insufficient oxygen will not.

## Problems

In the problems in this section, assume all gases are ideal.

A person hits a tennis ball with a mass of 0.058 kg against a wall. The average component of the ball’s velocity perpendicular to the wall is 11 m/s, and the ball hits the wall every 2.1 s on average, rebounding with the opposite perpendicular velocity component. (a) What is the average force exerted on the wall? (b) If the part of the wall the person hits has an area of $3.0\phantom{\rule{0.2em}{0ex}}{\text{m}}^{2},$ what is the average pressure on that area?

a. 0.61 N; b. 0.20 Pa

A person is in a closed room (a racquetball court) with $V=453\phantom{\rule{0.2em}{0ex}}{\text{m}}^{3}$ hitting a ball $\left(m=42.0\phantom{\rule{0.2em}{0ex}}\text{g}\right)$ around at random without any pauses. The average kinetic energy of the ball is 2.30 J. (a) What is the average value of ${v}_{x}^{2}?$ Does it matter which direction you take to be x ? (b) Applying the methods of this chapter, find the average pressure on the walls? (c) Aside from the presence of only one “molecule” in this problem, what is the main assumption in Pressure, Temperature, and RMS Speed that does not apply here?

Five bicyclists are riding at the following speeds: 5.4 m/s, 5.7 m/s, 5.8 m/s, 6.0 m/s, and 6.5 m/s. (a) What is their average speed? (b) What is their rms speed?

a. 5.88 m/s; b. 5.89 m/s

Some incandescent light bulbs are filled with argon gas. What is ${v}_{\text{rms}}$ for argon atoms near the filament, assuming their temperature is 2500 K?

Typical molecular speeds $\left({v}_{\text{rms}}\right)$ are large, even at low temperatures. What is ${v}_{\text{rms}}$ for helium atoms at 5.00 K, less than one degree above helium’s liquefaction temperature?

177 m/s

What is the average kinetic energy in joules of hydrogen atoms on the $5500\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ surface of the Sun? (b) What is the average kinetic energy of helium atoms in a region of the solar corona where the temperature is $6.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{K}$ ?

What is the ratio of the average translational kinetic energy of a nitrogen molecule at a temperature of 300 K to the gravitational potential energy of a nitrogen-molecule−Earth system at the ceiling of a 3-m-tall room with respect to the same system with the molecule at the floor?

$4.54\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}$

What is the total translational kinetic energy of the air molecules in a room of volume $23\phantom{\rule{0.2em}{0ex}}{\text{m}}^{3}$ if the pressure is $9.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\phantom{\rule{0.2em}{0ex}}\text{Pa}$ (the room is at fairly high elevation) and the temperature is $21\phantom{\rule{0.2em}{0ex}}\text{°C}$ ? Is any item of data unnecessary for the solution?

The product of the pressure and volume of a sample of hydrogen gas at $0.00\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ is 80.0 J. (a) How many moles of hydrogen are present? (b) What is the average translational kinetic energy of the hydrogen molecules? (c) What is the value of the product of pressure and volume at $200\phantom{\rule{0.2em}{0ex}}\text{°}\text{C?}$

a. 0.0352 mol; b. $5.65\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-21}\phantom{\rule{0.2em}{0ex}}\text{J;}$ c. 139 J

What is differential form of Gauss's law?
help me out on this question the permittivity of diamond is 1.46*10^-10.( a)what is the dielectric of diamond (b) what its susceptibility
a body is projected vertically upward of 30kmp/h how long will it take to reach a point 0.5km bellow e point of projection
i have to say. who cares. lol. why know that t all
Jeff
is this just a chat app about the openstax book?
kya ye b.sc ka hai agar haa to konsa part
what is charge quantization
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
determine absolute zero
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
U can easily calculate work done by 2.303log(v2/v1)
Abhishek
Amount of heat added through q=ncv^delta t
Abhishek
Change in internal energy through q=Q-w
Abhishek
please how do dey get 5/9 in the conversion of Celsius and Fahrenheit
what is copper loss
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
what is the weight of the earth in space
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.
explain the lack of symmetry in the field of the parallel capacitor
pls. explain the lack of symmetry in the field of the parallel capacitor
Phoebe