# 2.4 Distribution of molecular speeds  (Page 5/9)

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(a) Use the ideal gas equation to estimate the temperature at which 1.00 kg of steam (molar mass $M=18.0\phantom{\rule{0.2em}{0ex}}\text{g/mol}$ ) at a pressure of $1.50\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}\phantom{\rule{0.2em}{0ex}}\text{Pa}$ occupies a volume of $0.220\phantom{\rule{0.2em}{0ex}}{\text{m}}^{3}$ . (b) The van der Waals constants for water are $a=0.5537\phantom{\rule{0.2em}{0ex}}\text{Pa}·{\text{m}}^{6}\text{/}{\text{mol}}^{2}$ and $b=3.049\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\phantom{\rule{0.2em}{0ex}}{\text{m}}^{3}\text{/}\text{mol}$ . Use the Van der Waals equation of state to estimate the temperature under the same conditions. (c) The actual temperature is 779 K. Which estimate is better?

One process for decaffeinating coffee uses carbon dioxide $\left(M=44.0\phantom{\rule{0.2em}{0ex}}\text{g/mol}\right)$ at a molar density of about $14,600\phantom{\rule{0.2em}{0ex}}{\text{mol/m}}^{3}$ and a temperature of about $60\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ . (a) Is CO 2 a solid, liquid, gas, or supercritical fluid under those conditions? (b) The van der Waals constants for carbon dioxide are $a=0.3658\phantom{\rule{0.2em}{0ex}}\text{Pa}·{\text{m}}^{6}\text{/}{\text{mol}}^{2}$ and $b=4.286\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\phantom{\rule{0.2em}{0ex}}{\text{m}}^{3}\text{/}\text{mol}\text{.}$ Using the van der Waals equation, estimate the pressure of ${\text{CO}}_{2}$ at that temperature and density.

a. supercritical fluid; b. $3.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{7}\phantom{\rule{0.2em}{0ex}}\text{Pa}$

On a winter day when the air temperature is $0\phantom{\rule{0.2em}{0ex}}\text{°C},$ the relative humidity is $50%$ . Outside air comes inside and is heated to a room temperature of $20\phantom{\rule{0.2em}{0ex}}\text{°C}$ . What is the relative humidity of the air inside the room. (Does this problem show why inside air is so dry in winter?)

On a warm day when the air temperature is $30\phantom{\rule{0.2em}{0ex}}\text{°C}$ , a metal can is slowly cooled by adding bits of ice to liquid water in it. Condensation first appears when the can reaches $15\phantom{\rule{0.2em}{0ex}}\text{°C}$ . What is the relative humidity of the air?

$40.18%$

(a) People often think of humid air as “heavy.” Compare the densities of air with $0%$ relative humidity and $100%$ relative humidity when both are at 1 atm and $30\phantom{\rule{0.2em}{0ex}}\text{°C}$ . Assume that the dry air is an ideal gas composed of molecules with a molar mass of 29.0 g/mol and the moist air is the same gas mixed with water vapor. (b) As discussed in the chapter on the applications of Newton’s laws, the air resistance felt by projectiles such as baseballs and golf balls is approximately ${F}_{\text{D}}=C\rho A{v}^{2}\text{/}2$ , where $\rho$ is the mass density of the air, A is the cross-sectional area of the projectile, and C is the projectile’s drag coefficient. For a fixed air pressure, describe qualitatively how the range of a projectile changes with the relative humidity. (c) When a thunderstorm is coming, usually the humidity is high and the air pressure is low. Do those conditions give an advantage or disadvantage to home-run hitters?

The mean free path for helium at a certain temperature and pressure is $2.10\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-7}\phantom{\rule{0.2em}{0ex}}\text{m}\text{.}$ The radius of a helium atom can be taken as $1.10\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-11}\phantom{\rule{0.2em}{0ex}}\text{m}$ . What is the measure of the density of helium under those conditions (a) in molecules per cubic meter and (b) in moles per cubic meter?

a. $2.21\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{27}\phantom{\rule{0.2em}{0ex}}{\text{molecules/m}}^{3};$ b. $3.67\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}{\text{mol/m}}^{3}$

The mean free path for methane at a temperature of 269 K and a pressure of $1.11\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{Pa}$ is $4.81\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-8}\phantom{\rule{0.2em}{0ex}}\text{m}\text{.}$ Find the effective radius r of the methane molecule.

In the chapter on fluid mechanics, Bernoulli’s equation for the flow of incompressible fluids was explained in terms of changes affecting a small volume dV of fluid. Such volumes are a fundamental idea in the study of the flow of compressible fluids such as gases as well. For the equations of hydrodynamics to apply, the mean free path must be much less than the linear size of such a volume, $a\approx d{V}^{1\text{/}3}.$ For air in the stratosphere at a temperature of 220 K and a pressure of 5.8 kPa, how big should a be for it to be 100 times the mean free path? Take the effective radius of air molecules to be $1.88\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-11}\phantom{\rule{0.2em}{0ex}}\text{m},$ which is roughly correct for ${\text{N}}_{2}$ .

8.2 mm

what is calorimeter
heat measuring device
Suvransu
What is mean electric potential
Electric density formula
Int E•dA
Vineet
what is relation betweeen potential energy of a system and work done in bringing last chaege from infinity
Einstein and his general theory of relativity, a very nice concept,which revolutionize our modern world.
what's the theory of relativity?
Piyali
it related to universe time period
jyotirmayee
it is a theory in which time is taken as relative,for diff. motion of objects.
Antares
no !!!
jyotirmayee
it is E=mc'square
jyotirmayee
what is black hole?
jyotirmayee
E=mc^2 is just a reln which sums up everything dude
Antares
what does e=mc^2 stand for?explain
Piyali
m not dude
jyotirmayee
e for speed of light
jyotirmayee
c for speed of light
jyotirmayee
m for mass of object
jyotirmayee
black hole is a super massive object in space gravitation pull of which s so strong dt evn light cannot escape. John wheeler 1st detected it, n concept of it ws given by Einstein himself from his general theory of relativity. Basically v cn si 3 types of it super massive, interstellar n intermediate
Antares
which topic now u studying?
jyotirmayee
e defined? sorry it,s wrong
jyotirmayee
Why?
Arzoodan
how black holes r formed?
Piyali
e is not speed of light
jyotirmayee
black holes formed when the centre of very massive star collapsed itself
jyotirmayee
e is energy.
Antares
what do u mean by quantum mechanics?
jyotirmayee
in most of d cases black holes r formed by massive collapsed star or star system
Antares
sahoo u don't seem to understand relative physics, plz study that first.
Antares
exatly...
Arzoodan
Apollo is the name of a satellite !!!!!
jyotirmayee
quantum mechanics is d study of physics describing nature at d smallest level of energy of atoms n subatomic particles.
Antares
qm means explains about the microscopic particles..
KRANTHI
nope name of d sun god
Antares
why the mercury used in thermometers?
jyotirmayee
Ali brother ur exactly spelling is wrong,,,,,
jyotirmayee
why the colour of tube light white?
jyotirmayee
why the mouth became red colour ,,by the regular eating of leaf called ,,betel combining with areca?
jyotirmayee
all formula for calculate specific latent heat of any substance
hello
Nigar
Hi, your real Nigga...? Or this jock?
Arzoodan
real
Nigar
You from Pakistan or India?
Arzoodan
c'mon guys.. let's talk Physics.
Yoblaze
mass multiplied with latent heat of a substance
Yoblaze
Arzoodan
you both?
jyotirmayee
in which class?
jyotirmayee
physics is the only subject which underestimated chemistry ,,bio
jyotirmayee
how capacitor is made in inst?
Piyali
what is dipole moment
it is the product of electric charges and distance between the two charges
Shikhar
Arzoodan
mishra true thanks dia
Ssempala
product of separation of the poles, the rest shikhar got is right
brad is separation and distance ,are they different?
Ssempala
What is dielectric
its a type of medium. generally poor conductors. but their conductivity can be changed
vedanth
you just have to add impurities
vedanth
Thanks
Ssempala
grt
Ssempala
a material which behave as conductor
Shikhar
insulating material, energy level for electron transfer is very high e.g used to increase a magnetic field in a capacitor
What is the difference between specific heat capacity and heat capacity? Give the equations
presentation on power
relation between Celsius and Kelvin
0" degree Celsius=273kelvin
jyotirmayee
Newton's second laws is call with
what is mean by thermodynamics
it is study about temperature and it's equilibrium
thiru
Its the study of heat and its relation with others kind of energy
Antonio
state caulombs law clearly
show mathematically that an electron has the greater speed than the proton when they attract each other
show mathematically that an electron has the greater speed than the proton when they attract each other
srikanta
@ezra & srikanta; for electrons: a=ke^2/(mr^2) and for protons: a=kp^2/(mr^2)
Sikandar