Question

1-

A) A gas bottle contains 7.15×10^{23} Nitrogen molecules
at a temperature of 342.0 K. What is the thermal energy of the gas?
(You might need to know Boltzmann's constant: k_{B} =
1.38×10^{-23} J/K.)

B) How much energy is stored in ONE degree of freedom for the whole system?

C) What is the average energy of a single molecule?

D) On average how much energy is stored by ONE degree of freedom for ONE single molecule?

Answer #1

A gas bottle contains 5.40×1023 Hydrogen molecules at a
temperature of 350 K. What is the thermal energy of the gas? (You
might need to know Boltzmann's constant: kB = 1.38×10-23 J/K.)
Answer: 6.52×103 J
How much energy is stored in ONE degree of freedom for the whole
system?
What is the average energy of a single molecule?
Answer: 1.21×10-20 J
On average how much energy is stored by ONE degree of freedom
for ONE single molecule?

A gas bottle contains 4.90×1023 Hydrogen molecules at
a temperature of 368.0 K. What is the thermal energy of the gas?
(You might need to know Boltzmann's constant: kB =
1.38×10-23 J/K.)
Tries 0/12
How much energy is stored in ONE degree of freedom for the whole
system?
Tries 0/12
What is the average energy of a single molecule?
Tries 0/12
On average how much energy is stored by ONE degree of freedom
for ONE single molecule?

A gas bottle contains 9.94×1023 Hydrogen molecules at a
temperature of 339.0 K. What is the thermal energy of the gas? (You
might need to know Boltzmann's constant: kB = 1.38×10-23 J/K.)
Tries 0/20
How much energy is stored in ONE degree of freedom for the whole
system? Tries 0/20
What is the average energy of a single molecule? Tries 0/20
On average how much energy is stored by ONE degree of freedom
for ONE single molecule? Tries 0/20

1. Estimate the following for a nitrogen molecule. The diameter
of a nitrogen molecule is approximately 0.300 nm.
Estimate the mean free path of a nitrogenmolecule in air at the
top of Mt. Everest (altitude = 8.80 km, P ≈ 50.0 kPa, and
T ≈ 238 K). Value of Boltzmann's constant is
1.381×10−23 J/K (answer is in nm)
3. A tank of compressed air of volume 1.00 m3 is
pressurized to 27.0 atm at T = 273 K. A valve...

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 ×
10-26 kg and can move in three dimensions, rotate in two
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)
times the number of moles of the gas.
a) How...

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...

1.What is the RMS speed of Helium atoms when the temperature of
the Helium gas is 209 K? (Possibly useful constants: the atomic
mass of Helium is 4.00 AMU, the Atomic Mass Unit is: 1 AMU =
1.66×10-27 kg,constant is: kB = 1.38×10-23 J/K.)
2.What would be the RMS speed, if the temperature of the Helium
gas was doubled?

The average kinetic energy of the molecules in a gas
sample depends only on the temperature, T. However, given the same
kinetic energies, a lighter molecule will move faster than a
heavier molecule, as shown in the equation for rms speed rms
speed=√3RTM where R=8.314 J/(mol⋅K) and M is molar mass in
kilograms per mole. Note that a joule is the same as a
kilogram‑meter squared per second squared (kg·m2/s2). What is the
rms speed of Cl2 molecules at 471...

During hibernation, an animal’s metabolism slows down, and its
body temperature lowers. For example, a California ground
squirrel’s body temperature lowers from 40.0°C to 18.5°C during
hibernation. If we assume that the air in the squirrel’s lungs is
75.0% N2 and 25.0% O2, by how much will the
rms speed of the air molecules in the lungs have decreased during
hibernation? Boltzmann's constant is 1.38 × 10−23 J/K.
Molar mass of Nitrogen is 14.00674 u and Oxygen is 15.9994 u....

A cylinder contains 1.5 moles of ideal gas, initially at a
temperature of 113 ∘C. The cylinder is provided with a frictionless
piston, which maintains a constant pressure of 6.4×105Pa on the
gas. The gas is cooled until its temperature has decreased to 27∘C.
For the gas CV = 11.65 J/mol⋅K, and the ideal gas
constant R = 8.314 J/mol⋅K.
1.Find the work done by the gas during this process.
2.What is the change in the internal (thermal) energy of...

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