# 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 thermodynamics
the study of heat an other form of energy.
John
heat is internal kinetic energy of a body but it doesnt mean heat is energy contained in a body because heat means transfer of energy due to difference in temperature...and in thermo-dynamics we study cause, effect, application, laws, hypothesis and so on about above mentioned phenomenon in detail.
ing
It is abranch of physical chemistry which deals with the interconversion of all form of energy
Vishal
what is colamb,s law.?
it is a low studied the force between 2 charges F=q.q\r.r
Mostafa
what is the formula of del in cylindrical, polar media
prove that the formula for the unknown resistor is Rx=R2 x R3 divided by R3,when Ig=0.
what is flux
Total number of field lines crossing the surface area
Kamru
Basically flux in general is amount of anything...In Electricity and Magnetism it is the total no..of electric field lines or Magnetic field lines passing normally through the suface
prince
what is temperature change
Celine
a bottle of soft drink was removed from refrigerator and after some time, it was observed that its temperature has increased by 15 degree Celsius, what is the temperature change in degree Fahrenheit and degree Celsius
Celine
process whereby the degree of hotness of a body (or medium) changes
Salim
Q=mcΔT
Salim
where The letter "Q" is the heat transferred in an exchange in calories, "m" is the mass of the substance being heated in grams, "c" is its specific heat capacity and the static value, and "ΔT" is its change in temperature in degrees Celsius to reflect the change in temperature.
Salim
what was the temperature of the soft drink when it was removed ?
Salim
15 degree Celsius
Celine
15 degree
Celine
ok I think is just conversion
Salim
15 degree Celsius to Fahrenheit
Salim
0 degree Celsius = 32 Fahrenheit
Salim
15 degree Celsius = (15×1.8)+32 =59 Fahrenheit
Salim
I dont understand
Celine
the question said you should convert 15 degree Celsius to Fahrenheit
Salim
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
Salim
what is d final ans for Fahrenheit and Celsius
Celine
it said what is temperature change in Fahrenheit and Celsius
Celine
the 15 is already in Celsius
Salim
So the final answer for Fahrenheit is 59
Salim
what is d final ans for Fahrenheit and Celsius
Celine
what are the effects of placing a dielectric between the plates of a capacitor
increase the capacitance.
Jorge
besides increasing the capacitance, is there any?
Bundi
mechanical stiffness and small size
Jorge
why for an ideal gas internal energy is directly proportional to thermodynamics temperature?
two charged particles are 8.45cm apart. They are moved and the force on each of them is found to have tripled. How far are they now?
what is flux
Bundi
Bundi, flux is the number of electric field crossing a surface area
Mubanga
you right
martin,F/F=(r×r)÷(r×r)
Mostafa
determining dimensional correctness
determine dimensional correctness of,T=2π√L/g
PATRICK
somebody help me answer the question above
PATRICK
d=dQ+w
calculate the heat flow per square meter through a mineral roll insulation 5cm thick if the temperature on the two surfaces are 30degree Celsius and 20 degree Celsius respectively. thermal conduction of mineral roll is 0.04
what are the elementary compositions of a cell?
poles, chemical
prabir
when a current pass through a material does the velocity varies
no.
prabir
what is spin entropy ?and disorder in ferromagnetic material
diagram of an hall effect sensor
if a magnetised wire having dipole moment M is bent in the form of arc subtending angle of 45°at centre,new magnetic moment is
prabir