Question

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 many degrees of freedom does each molecule of the gas have?

b) What is the internal energy of the gas?

c) What is the average translational speed of the gas molecules?

d) The gas cools to a temperature 524 K, which causes the gas atoms to stop vibrating, but maintain their translational and rotational modes of motion. What is the change in the internal energy of the gas?

Answer #1

(a) three dimensions, rotate in two dimensions, and vibrate in one dimension

means

degree of freedom = 6

----------------------

(b)

U = (N/2) * n * T

where N is degree of freedom

U = (6/2) * 4.8 * 8.314 * 1061

U = 127024.62 J

---------------------------

(c)

v = sqrt ( 3RT / m)

where m = 2.32e-26 * 6.022e23 = 0.01397

so,

v = sqrt ( 3 * 8.314 * 1061 / 0.01397)

v = 1376.28 m/s

----------------------------------------------------

(d)

now, when T = 524 K

One degree of freedom will decrease as it stops vibrating, so we have only 5 degree of freedom

U ( new) = (5/2) * 4.8 * 8.314 * 524

U = 52278.4 J

so,

change in the internal energy of the gas = 52278.4 J - 127024.62

change in the internal energy of the gas = - 74746.2 J

Suppose that 2.8 moles of an ideal diatomic gas has a
temperature of 1003 K, and that each molecule has a mass 2.32

Neon gas (a monatomic gas) and hydrogen gas (a diatomic gas) are
both held at constant volume in separate containers. Each container
contains the same number of moles n of each gas. You find
that it takes an input of 300 J of heat to increase the temperature
of the hydrogen by 2.50°C.
Part A
How many modes does a single hydrogen gas molecule have? (Assume
the vibrational modes are "frozen out").
3, all rotational kinetic
6, 3 translational kinetic...

Consider 14.61 moles of an ideal diatomic gas. (a) Find the
total heat capacity of the gas at (i) constant volume and (ii)
constant pressure assuming that the molecules translate and vibrate
but do not rotate. Be sure to clearly explain how the equipartition
of energy is used to solve this problem. (b) Repeat problem (a)
above except assume that the molecules translate, rotate and
vibrate.

Which of the following statements are true? A.The number of
moles in 1.00 atm of gas was the same, despite the fact that the
gases themselves had different identities. B.The number of moles in
1.00 atm of gas varied linearly with increasing molar mass. C.The
volume of the gas varied depending on the identity of the gas.
D.The number of moles in 1.00 atm of gas varied hyperbolically with
increasing molar mass.
Given Avogadro's Law, which of the following statements...

Ivan heats at constant pressure 2.10 moles of a diatomic gas
starting at 300K. For this gas,
the molecules vibrate
above 500K. A total of 20,000J of heat is put into the
gas during this process.
a) Clearly show that the final temperature of the gas is TF =
599K.
b) How many joules of the (20,000J of) heat went into increasing
the kinetic energy of translation?
c) How many joules of the heat went into increasing the energies
associated...

Ivan heats at constant pressure 2.10 moles of a diatomic gas
starting at 300K. For this gas, the molecules vibrate above 500K. A
total of 20,000J of heat is put into the gas during this process.
a) Clearly show that the final temperature of the gas is TF = 599K.
b) How many joules of the (20,000J of) heat went into increasing
the kinetic energy of translation? c) How many joules of the heat
went into increasing the energies associated...

Rectangular PV Cycle
A piston contains 260 moles of an ideal monatomic gas that
initally has a pressure of 2.61 × 105 Pa and a volume of
4.9 m3. The piston is connected to a hot and cold
reservoir and the gas goes through the following quasi-static cycle
accepting energy from the hot reservoir and exhausting energy into
the cold reservoir.
1. The pressure of the gas is increased to 5.61 × 105
Pa while maintaining a constant volume.
2....

The number of moles in a sample of diatomic gas molecules is
such that nR = 300 J/K. The initial volume of this sample of gas is
Va, and its initial temperature is Ta =250 K. The volume of this
sample of gas is doubled (Vb =2 Va) in a constant pressure
(isobaric) process and its temperature increases to Tb. What is the
change in entropy DS of this gas sample as a result of the isobaric
expansion to a...

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),...

1-
A) A gas bottle contains 7.15×1023 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: kB =
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?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 7 minutes ago

asked 20 minutes ago

asked 29 minutes ago

asked 30 minutes ago

asked 32 minutes ago

asked 40 minutes ago

asked 42 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago