Question

3. Estimate for yourself, without using the Internet:

a) the number of air molecules in a classroom

b) the volume per molecule in the room

c) the average distance between molecules in the room (starting from the answer to part b).

Answer #1

At 20 ∘C (approximately room temperature) the average velocity
of N2 molecules in air is 1050 mph.
Part A What is the kinetic energy (in J) of an N2 molecule
moving at this speed? Express your answer using four significant
figures.
Part B What is the total kinetic energy of 1 mol of N2 molecules
moving at this speed? Express your answer using four significant
figures.

Estimate the number of air molecules striking your face in a
second at room temperature.

6. (a) Find the de Broglie wavelength of a nitrogen molecule in
air at room temperature
(293K). (b) The density of air at room temperature and atmospheric
pressure is 1.292
kg/m3. Find the average distance between air molecules at this
temperature and
compare with the de Broglie wavelength. What do you conclude about
the importance
of quantum effects in air at room temperature? (c) Estimate the
temperature at which
quantum effects might become important.

Consider a classroom filled with air. Let’s approximate air as
an ideal gas of N2-molecules (nitrogen) at normal conditions (P = 1
Bar and T = 300 Kelvin). Suppose the room has dimensions of 10 m by
10 m by 10 m (a pretty large auditorium). Let us also assume that
N2 molecule has 5 degrees of freedom (3 translational and 2
rotational). In this problem you will need to provide numeric
answers up to the first significant digit.
2.1...

Problem 5.91 At 20 ∘C (approximately room temperature) the
average velocity of N2 molecules in air is 1050 mph. Part C What is
the total kinetic energy of 1 mol of N2 molecules moving at this
speed? Express your answer using four significant figures.

suppose your room volume is 41m^3. One mole of an ideal gas at STP
occupies a volume of 22.4 L
a) estimate the number of moles of air in your room
b) how many molecules is that?
c) there are N^N ways to distribute N things onto N sites. As
a rough approximation, assume there are as many states for air
molecules as there are air molecules in your room. Compute the
entropy of the air in your room.

Calculate the number of
molecules in a deep breath of air whose volume is 2.35
L at body temperature, 36
∘C,
and a pressure of 735
torr.
Express
the answer in molecules to three significant figures.
The adult
blue whale has a lung capacity of
5.0×103
L. Calculate the mass of air (assume an average molar
mass 28.98
g/mol)
contained in an adult blue whale’s lungs at 0.5
∘C
and 1.10
atm,
assuming the air behaves ideally.
Express the answer...

The dimensions of a classroom are 4.70 m ? 2.55 m ? 2.90 m.
(a) Find the number of molecules of air in the classroom at
atmospheric pressure and 18.0°C.
molecules
(b) Find the mass of this air, assuming the air consists of
diatomic molecules with molar mass 28.9 g/mol.
kg
(c) Find the average kinetic energy of the molecules.
J
(d) Find the rms molecular speed.
m/s
(e) Assume the molar specific heat of the air is independent of...

(a) The density of the interstellar gas, mainly hydrogen (2
g/mol), is approximately one molecule (2 g/mol).
per cubic centimeter. If the molar diameter is 10-10 m, what is the
average free path? What is the
the collision frequency for a hydrogen molecule if the temperature
is 3 K?
(b) It has been seen that for diffusion, the distance travelled
by a molecule is proportional to the root of the molecule.
square of the number n of collisions, i.e. the...

At 200 °C, a box with a pressure of 3 atmospheres contains 36gm
of nitrogen. Show your work.
a) How many moles of gas is in the container?
b) What is the volume that this gas occupies?
c) Assuming that the container has a cubic shape, what will be
the total number of molecules?
d) What is the mean distance between the molecules?
e) What is the average speed of the nitrogen molecules?
f) Let's assume that using a piston...

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