Ing. Industrial

Chapter 17
Temperature and the Kinetic Theory of Gases
Conceptual Problems
*1 •
(a) False. If two objects are in thermal equilibrium with a third, then they are in thermal
equilibrium with each other.
(b) False. The Fahrenheit and Celsius temperature scales differ in the number of intervals
between the ice-point temperature and the steam-point temperature.
(c) True.
(d) False. The resultone obtains for the temperature of a given system is thermometerdependent.
2 •
Determine the Concept Put each in thermal equilibrium with a third body; e.g., a
thermometer. If each body is in thermal equilibrium with the third, then they are in
thermal equilibrium with each other.
3 •
Picture the Problem We can decide which room was colder by converting 20°F to the
equivalent Celsiustemperature.
Using the Fahrenheit-Celsius conversion,
convert 20°F to the equivalent Celsius
temperature:
( ) ( )
6.67 C
32 20 32 9
5
9 F
5
C
= − °
t = t − ° = ° − °
so Mert's room was colder.
4 ••
Picture the Problem We can apply the ideal-gas law to the two vessels to decide which
of these statements is correct.
Apply the ideal-gas law to the
particles in vessel 1:
1 1 1 1 PV = NkT
Apply the ideal-gas law to the
particles in vessel 2:
2 2 2 2 PV = N kT
Divide the equation for vessel 1 by
the equation for vessel 2: 2 2
1 1
2 2
1 1
N kT
N kT
PV
PV =
1314 Chapter 17
Because the vessels are identical and
are at the same temperature and
pressure:
2
1 1
N
= N and 1 2 N = N
(a)is correct.
5 ••
Determine the Concept From the ideal-gas law, we have P = nRT V. In the process
depicted, both the temperature and the volume increase, but the temperature increases
faster than does the volume. Hence, the pressure increases.
*6 ••
Determine the Concept From the ideal-gas law, we have V = nRT P. In the
process depicted, both the temperature and the pressure increase, but the pressure
increases faster than does the temperature. Hence, the volumedecreases.
7 •
True. The kinetic energy of translation K for n moles of gas is directly proportional to the
absolute temperature T of the gas (K nkT ) 2
3 = .
8 •
Determine the Concept We can use v 3RT M rms = to relate the temperature of a gas
to the rms speed of its molecules.
Express the dependence of the rms
speed of the molecules of a gas on
their absolute temperature:
M
v 3RT
rms =where R is the gas constant, M is the molar
mass, and T is the absolute temperature.
to double the rms speed of the molecules.
Because , the temperaturemust be quadrupled in order rms v ∝ T
9 •
Picture the Problem The average kinetic energy of a molecule, as a function of the
temperature, is given by K kT 2
3
av = and the pressure, volume, and temperature of an ideal
gas are relatedaccording to PV = NkT.
Express the average kinetic energy
of a molecule in terms of its
temperature:
K kT 2
3
av =
Temperature and the Kinetic Theory of Gases 1315
From the ideal-gas law we have: PV = NkT
Eliminate kT between these
equations to obtain: N
K PV
2
3
av =
If is doubled at constant , increases by a factor of 2. av P V K
If is doubled at constant , increases by a factor of 2. avV P K
10 ••
Picture the Problem We can express the rms speeds of the helium atoms and the
methane molecules using 3 . rms v = RT M
Express the rms speed of the
helium atoms: ( )
He
rms
He 3
M
v = RT
Express the rms speed of the
methane molecules: ( )
CH4
rms 4
CH 3
M
v = RT
Divide the first of these equations
by the second to obtain:
( )
( ) He
CH
rms 4
rms 4
CH
He
M
Mv
v =
Use Appendix C to find the molar
masses of helium and methane:
( )
( ) 2
4g/mol
16g/mol
CH
He
rms 4
rms = =
v
v
and (b) is correct.
11 •
False. Whether the pressure changes also depends on whether and how the volume
changes. In an isothermal process, the pressure can increase while the volume decreases
and the temperature is constant.
12 •
Determine the Concept For...