Question

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?

Answer #1

a) Thermal energy of the gas (all molecules) is

(Taking into account degrees of freedom for hydrogen molecules as diatomic gas, f = 5)

b) In one degree of freedom, energy stored is 1/5 th of above.

c) For average energy of a single molecule, divide (a) by N, we get

d) For one single molecule in one degree of freedom,

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?

An insulated bottle contains 1 mole of hydrogen gas at P=1 atm
and T=300K. Using a magic wand, you order all covalent bonds in the
H2 molecules to break instantly. Assume that the magic wand
supplies precisely the amount of energy necessary to br eak the
bond in every molecule and makes them chemically inert (so they
cant recombine) but does not affect the hydrogen otherwise. When
the new equilibrium is established,
a) What is the new temperature of the...

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...

An insulated bottle contains 1 mole of hydrogen gas at P=1 atm
and T=300K. Using a magic wand, you order all covalent bonds in the
H2 molecules to break instantly. Assume that the magic wand
supplies precisely the amount of energy necessary to br eak the
bond in every molecule and makes them chemically inert (so they
cant recombine) but does not affect the hydrogen otherwise. When
the new equilibrium is established,
a) What is the new temperature of the...

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