Question

Consider a gas which is not ideal so that molecules do interact with each other. this gas is in thermal equilibrium at the absolute temperature T. suppose that the translational degrees of freedom of this gas can be treated classically. what is the mean kinetic energy of (center-of-mass) translation of a molecule in this gas?

Answer #1

Q.1 (1) For one mol of a
monoatomic ideal gas in thermal equilibrium derive an expression
for the total kinetic energy of all molecules as a function of
temperature. Assume three degrees of freedom for each molecule due
to translational motion. Explain how your result is related to the
equipartition
theorem.

Suppose that 4.8 moles of an ideal diatomic gas has a
temperature of 1061 K, and that each molecule has a mass 2.32 ×
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dimensions, and vibrate in one dimension as the bond between the
atoms stretches and compresses. It may help you to recall that the
number of gas molecules is equal to Avagadros number (6.022 × 1023)
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a) How...

Consider a gas of nitrogen molecules at 20°C with a particle
density of 2.7 ×1019 molecules/cm3. The molar mass of
nitrogen molecules is 28 g/mol.(a) What is the rms speed of the
nitrogen molecules?(b) At what temperature will the rms speed be
half that value?(c) What is the average translational kinetic
energy of these molecules at 20°C? (d) The mean free path of the
nitrogen molecules is 0.80×10−5 cm. What is the molecular radius of
a nitrogen molecule?

12a. Two moles of an ideal gas are placed in a container whose
volume is 3.7 x 10-3 m3. The absolute pressure of the gas is 7.2 x
105 Pa. What is the average translational kinetic energy of a
molecule of the gas? Number Entry field with incorrect answer now
contains modified data Units Entry field with correct answer
b. Two ideal gases have the same mass density and the same
absolute pressure. One of the gases is helium (He),...

Photons are massless light particles and they do not interact
with each other. Consider a gas of N photons in volume V at
temperature T. The energy e of a photon is related to its momentum
p by the equation e = cp, where c is the speed of light. Find the
pressure P and the internal energy E of the photon gas in terms of
N, V, T, and k.
' Hint: ? = −??????, where the partition function...

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...

1. The average kinetic energy of the molecules in a gas sample
depends only on the temperature, T. But given the same kinetic
energies, a lighter molecule will move faster than a heavier
molecule.
A. What is the rms speed of Cl2 molecules at 505 K?
B. What is the rms speed of He atoms at 505 K?
2. Use the van der Waals equation of state to calculate the
pressure of 3.70 mol of H2O at 473 K in...

2 Equipartition The laws of statistical mechanics lead to a
surprising, simple, and useful result — the Equipartition Theorem.
In thermal equilibrium, the average energy of every degree of
freedom is the same: hEi = 1 /2 kBT. A degree of freedom is a way
in which the system can move or store energy. (In this expression
and what follows, h· · ·i means the average of the quantity in
brackets.) One consequence of this is the physicists’ form of...

Consider a gas in equilibrium with a surface. The surface can
adsorb the gas molecules onto any of M independent,
distinguishable sites (distinguishable because the binding
sites are localized to specific parts of the surface). The
molecular partition function for an adsorbed molecule is
q(T) ≡ exp[−β
Asurface].
a) Assume that the adsorbed molecules are independent and use
the canonical ensemble for N adsorbed molecules to compute
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to include the...

1. You have two identical containers, one containing gas A and
the other containing gas B. Both gases are under the same pressure
and are at 5.0 ?C. The molecular masses are mA = 3.29 × 10?27 kg
and mB = 6.12 × 10?26 kg.
(a) (1 point) Which gas has greater translational kinetic energy
per molecule?
(b) (1 point) Which gas has greater rms speed?
(c) (1 point) Assuming you can only change one of the
containers, the temperature...

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