A carbon nanotube is suspended across a trench of width s = 5 μm that separates two islands, each at T ∞ = 300 K . A focused laser beam irradiates the nanotube at a distance ξ from the left island, delivering q = 10 μW of energy to the nanotube. The nanotube temperature is measured at the midpoint of the trench using a point probe. The measured nanotube temperature is T 1 = 324.5 K for ξ 1 = 1.5 μm and T 2 = 326.4 K for ξ 2 = 3.5 μm . Determine the two contact resistances, R t , c , L and R t , c , R at the left and right ends of the nanotube, respectively. The experiment is performed in a vacuum with T sur = 300 K . The nanotube thermal conductivity and diameter are ken k cn = 3100 W/m ⋅ K and D = 14 nm, respectively.
A carbon nanotube is suspended across a trench of width s = 5 μm that separates two islands, each at T ∞ = 300 K . A focused laser beam irradiates the nanotube at a distance ξ from the left island, delivering q = 10 μW of energy to the nanotube. The nanotube temperature is measured at the midpoint of the trench using a point probe. The measured nanotube temperature is T 1 = 324.5 K for ξ 1 = 1.5 μm and T 2 = 326.4 K for ξ 2 = 3.5 μm . Determine the two contact resistances, R t , c , L and R t , c , R at the left and right ends of the nanotube, respectively. The experiment is performed in a vacuum with T sur = 300 K . The nanotube thermal conductivity and diameter are ken k cn = 3100 W/m ⋅ K and D = 14 nm, respectively.
Solution Summary: The author explains the thermal conductivities for both the laser irradiation locations.
A carbon nanotube is suspended across a trench of width
s
=
5
μm
that separates two islands, each at
T
∞
=
300
K
.
A focused laser beam irradiates the nanotube at a distance
ξ
from the left island, delivering
q
=
10
μW
of energy to the nanotube. The nanotube temperature is measured at the midpoint of the trench using a point probe. The measured nanotube temperature is
T
1
=
324.5
K
for
ξ
1
=
1.5
μm
and
T
2
=
326.4
K
for
ξ
2
=
3.5
μm
.
Determine the two contact resistances,
R
t
,
c
,
L
and
R
t
,
c
,
R
at the left and right ends of the nanotube, respectively. The experiment is performed in a vacuum with
T
sur
=
300
K
.
The nanotube thermal conductivity and diameter are ken
k
cn
=
3100
W/m
⋅
K
and
D
=
14
nm,
respectively.
The image shows a plane wall of thicknessΔx = 21 cm with a thermal conductivity k=0.7 W/(mK). Given that the temperature at point 2 is 283 K and that the heat flux from points 1 to 2 is 154 W/m2 calculate the temperature at point 1 in Kelvin to 1dp (decimal place
Nanotechnology, the field of building ultrasmall structures one atom at a time, has progressed in recent years. One potential application of nanotechnology is the construction of artificial cells. The simplest cells would probably mimic red blood cells, the body’s oxygen transporters. Nanocontainers, perhaps constructed of carbon, could be pumped full of oxygen and injected into a person’s bloodstream. If the person needed additional oxygen—due to a heart attack or for the purpose of space travel, for example—these containers could slowly release oxygen into the blood, allowing tissues that would otherwise die to remain alive. Suppose that the nanocontainers were cubic and had an edge length of 25 nanometers. Suppose that each nanocontainer could contain pure oxygen pressurized to a density of 85 g/L. How many grams of oxygen could be contained by each nanocontainer?
Nanotechnology, the field of building ultrasmall structures one atom at a time, has progressed in recent years. One potential application of nanotechnology is the construction of artificial cells. The simplest cells would probably mimic red blood cells, the body’s oxygen transporters. Nanocontainers, perhaps constructed of carbon, could be pumped full of oxygen and injected into a person’s bloodstream. If the person needed additional oxygen—due to a heart attack or for the purpose of space travel, for example—these containers could slowly release oxygen into the blood, allowing tissues that would otherwise die to remain alive. Suppose that the nanocontainers were cubic and had an edge length of 25 nanometers. What is the volume of one nanocontainer? (Ignore the thickness of the nanocontainer’s wall.)
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