# 2.2 Pressure, temperature, and rms speed  (Page 10/18)

 Page 10 / 18

What is the gauge pressure inside a tank of $4.86\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\phantom{\rule{0.2em}{0ex}}\text{mol}$ of compressed nitrogen with a volume of $6.56\phantom{\rule{0.2em}{0ex}}{\text{m}}^{3}$ if the rms speed is 514 m/s?

If the rms speed of oxygen molecules inside a refrigerator of volume $22.0\phantom{\rule{0.2em}{0ex}}\text{ft}{\text{.}}^{3}$ is 465 m/s, what is the partial pressure of the oxygen? There are 5.71 moles of oxygen in the refrigerator, and the molar mass of oxygen is 32.0 g/mol.

21.1 kPa

The escape velocity of any object from Earth is 11.1 km/s. At what temperature would oxygen molecules (molar mass is equal to 32.0 g/mol) have root-mean-square velocity ${v}_{\text{rms}}$ equal to Earth’s escape velocity of 11.1 km/s?

The escape velocity from the Moon is much smaller than that from the Earth, only 2.38 km/s. At what temperature would hydrogen molecules (molar mass is equal to 2.016 g/mol) have a root-mean-square velocity ${v}_{\text{rms}}$ equal to the Moon’s escape velocity?

458 K

Nuclear fusion, the energy source of the Sun, hydrogen bombs, and fusion reactors, occurs much more readily when the average kinetic energy of the atoms is high—that is, at high temperatures. Suppose you want the atoms in your fusion experiment to have average kinetic energies of $6.40\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-14}\phantom{\rule{0.2em}{0ex}}\text{J}$ . What temperature is needed?

Suppose that the typical speed $\left({v}_{\text{rms}}\right)$ of carbon dioxide molecules (molar mass is 44.0 g/mol) in a flame is found to be 1350 m/s. What temperature does this indicate?

$3.22\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{K}$

(a) Hydrogen molecules (molar mass is equal to 2.016 g/mol) have ${v}_{\text{rms}}$ equal to 193 m/s. What is the temperature? (b) Much of the gas near the Sun is atomic hydrogen (H rather than ${\text{H}}_{2}\right).$ Its temperature would have to be $1.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{7}\phantom{\rule{0.2em}{0ex}}\text{K}$ for the rms speed ${v}_{\text{rms}}$ to equal the escape velocity from the Sun. What is that velocity?

There are two important isotopes of uranium, ${}^{235}\text{U}$ and ${}^{238}\text{U}$ ; these isotopes are nearly identical chemically but have different atomic masses. Only ${}^{235}\text{U}$ is very useful in nuclear reactors. Separating the isotopes is called uranium enrichment (and is often in the news as of this writing, because of concerns that some countries are enriching uranium with the goal of making nuclear weapons.) One of the techniques for enrichment, gas diffusion, is based on the different molecular speeds of uranium hexafluoride gas, ${\text{UF}}_{6}$ . (a) The molar masses of ${}^{235}\text{U}$ and ${}^{238}{\text{UF}}_{6}$ are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their typical speeds ${v}_{\text{rms}}$ ? (b) At what temperature would their typical speeds differ by 1.00 m/s? (c) Do your answers in this problem imply that this technique may be difficult?

a. 1.004; b. 764 K; c. This temperature is equivalent to $915\phantom{\rule{0.2em}{0ex}}\text{ºF}$ , which is high but not impossible to achieve. Thus, this process is feasible. At this temperature, however, there may be other considerations that make the process difficult. (In general, uranium enrichment by gaseous diffusion is indeed difficult and requires many passes.)

The partial pressure of carbon dioxide in the lungs is about 470 Pa when the total pressure in the lungs is 1.0 atm. What percentage of the air molecules in the lungs is carbon dioxide? Compare your result to the percentage of carbon dioxide in the atmosphere, about 0.033%.

Dry air consists of approximately $78\text{%}\phantom{\rule{0.2em}{0ex}}\text{nitrogen},21\text{%}\phantom{\rule{0.2em}{0ex}}\text{oxygen},\text{and}\phantom{\rule{0.2em}{0ex}}1\text{%}\phantom{\rule{0.2em}{0ex}}\text{argon}$ by mole, with trace amounts of other gases. A tank of compressed dry air has a volume of 1.76 cubic feet at a gauge pressure of 2200 pounds per square inch and a temperature of 293 K. How much oxygen does it contain in moles?

65 mol

(a) Using data from the previous problem, find the mass of nitrogen, oxygen, and argon in 1 mol of dry air. The molar mass of ${\text{N}}_{2}$ is 28.0 g/mol, that of ${\text{O}}_{2}$ is 32.0 g/mol, and that of argon is 39.9 g/mol. (b) Dry air is mixed with pentane $\left({\text{C}}_{5}{\text{H}}_{12},$ molar mass 72.2 g/mol), an important constituent of gasoline, in an air-fuel ratio of 15:1 by mass (roughly typical for car engines). Find the partial pressure of pentane in this mixture at an overall pressure of 1.00 atm.

(a) Given that air is $21%$ oxygen, find the minimum atmospheric pressure that gives a relatively safe partial pressure of oxygen of 0.16 atm. (b) What is the minimum pressure that gives a partial pressure of oxygen above the quickly fatal level of 0.06 atm? (c) The air pressure at the summit of Mount Everest (8848 m) is 0.334 atm. Why have a few people climbed it without oxygen, while some who have tried, even though they had trained at high elevation, had to turn back?

a. 0.76 atm; b. 0.29 atm; c. The pressure there is barely above the quickly fatal level.

(a) If the partial pressure of water vapor is 8.05 torr, what is the dew point? $\left(760\phantom{\rule{0.2em}{0ex}}\text{torr}=1\phantom{\rule{0.2em}{0ex}}\text{atm}=101,325\phantom{\rule{0.2em}{0ex}}\text{Pa}\right)$ (b) On a warm day when the air temperature is $35\phantom{\rule{0.2em}{0ex}}\text{°C}$ and the dew point is $25\phantom{\rule{0.2em}{0ex}}\text{°C}$ , what are the partial pressure of the water in the air and the relative humidity?

what is principle of superposition
what are questions that are likely to come out during exam
what is electricity
watt is electricity.
electricity ka full definition with formula
Jyoti
If a point charge is released from rest in a uniform electric field will it follow a field line? Will it do so if the electric field is not uniform?
Maxwell's stress tensor is
Yes
doris
neither vector nor scalar
Anil
if 6.0×10^13 electrons are placed on a metal sphere of charge 9.0micro Coulombs, what is the net charge on the sphere
18.51micro Coulombs
ASHOK
Is it possible to find the magnetic field of a circular loop at the centre by using ampere's law?
Is it possible to find the magnetic field of a circular loop at it's centre?
yes
Brother
The density of a gas of relative molecular mass 28 at a certain temperature is 0.90 K kgmcube.The root mean square speed of the gas molecules at that temperature is 602ms.Assuming that the rate of diffusion of a gas in inversely proportional to the square root of its density,calculate the density of
A hot liquid at 80degree Celsius is added to 600g of the same liquid originally at 10 degree Celsius. when the mixture reaches 30 degree Celsius, what will be the total mass of the liquid?
Under which topic
doris
what is electrostatics
Study of charges which are at rest
himanshu
Explain Kinematics
Two equal positive charges are repelling each other. The force on the charge on the left is 3.0 Newtons. Using your notes on Coulomb's law, and the forces acting on each of the charges, what is the force on the charge on the right?
Using the same two positive charges, the left positive charge is increased so that its charge is 4 times LARGER than the charge on the right. Using your notes on Coulomb's law and changes to the charge, once the charge is increased, what is the new force of repulsion between the two positive charges?
Nya
A mass 'm' is attached to a spring oscillates every 5 second. If the mass is increased by a 5 kg, the period increases by 3 second. Find its initial mass 'm'
a hot water tank containing 50,000g of water is heated by an electric immersion heater rated at 3kilowatt,240volt, calculate the current
what is charge
product of current and time
Jaffar By Prateek Ashtikar By Mariah Hauptman By Joanna Smithback By Brooke Delaney By Brooke Delaney By JavaChamp Team By Richley Crapo By Joli Julianna By Michael Pitt By OpenStax