A method for determining the thermal conductivity k and the specific heat c p of a material is illustrated in the sketch. Initially the two identical samples of diameter D = 60 mm and thickness L = 10 mm and the thin heater are at a uniform temperature of T i = 23.00 ° C, while surrounded by an insulating powder. Suddenly the heater is energized to provide a uniform heat flux q o n on each of the sample interfaces, and the heat flux is maintained constant for a period of time, Δ t o . A short time after sudden heating is initiated, the temperature at this interface T o is related to the heat flux as T o ( t ) − T i = 2 q o n ( t π ρ c p k ) 1 / 2 For a particular test run, the electrical heater dissipates 15.0 W fora period of Δ t o = 120 s, and the temperature at the interface is t o ( 30 s ) = 24.57 ° C after 30s of heating. A long time after the heater is deenergized, t ≫ Δ t o , the samples reach the uniform temperature of T o ( ∞ ) = 33.50 ° C . The density of the sample materials, determined by measurement of volume and mass, is ρ = 3965 kg/m 3 . Determine the specific heat and thermal conductivity of the test material. By looking at values of the thermophysical properties in Table A.1 or A.2, identify the test sample material.
A method for determining the thermal conductivity k and the specific heat c p of a material is illustrated in the sketch. Initially the two identical samples of diameter D = 60 mm and thickness L = 10 mm and the thin heater are at a uniform temperature of T i = 23.00 ° C, while surrounded by an insulating powder. Suddenly the heater is energized to provide a uniform heat flux q o n on each of the sample interfaces, and the heat flux is maintained constant for a period of time, Δ t o . A short time after sudden heating is initiated, the temperature at this interface T o is related to the heat flux as T o ( t ) − T i = 2 q o n ( t π ρ c p k ) 1 / 2 For a particular test run, the electrical heater dissipates 15.0 W fora period of Δ t o = 120 s, and the temperature at the interface is t o ( 30 s ) = 24.57 ° C after 30s of heating. A long time after the heater is deenergized, t ≫ Δ t o , the samples reach the uniform temperature of T o ( ∞ ) = 33.50 ° C . The density of the sample materials, determined by measurement of volume and mass, is ρ = 3965 kg/m 3 . Determine the specific heat and thermal conductivity of the test material. By looking at values of the thermophysical properties in Table A.1 or A.2, identify the test sample material.
Solution Summary: The author explains the specific heat and thermal conductivity of the test material.
A method for determining the thermal conductivity k and the specific heat
c
p
of a material is illustrated in the sketch. Initially the two identical samples of diameter
D
=
60
mm
and thickness
L
=
10
mm
and the thin heater are at a uniform temperature of
T
i
=
23.00
°
C,
while surrounded by an insulating powder. Suddenly the heater is energized to provide a uniform heat flux
q
o
n
on each of the sample interfaces, and the heat flux is maintained constant for a period of time,
Δ
t
o
.
A short time after sudden heating is initiated, the temperature at this interface
T
o
is related to the heat flux as
T
o
(
t
)
−
T
i
=
2
q
o
n
(
t
π
ρ
c
p
k
)
1
/
2
For a particular test run, the electrical heater dissipates 15.0 W fora period of
Δ
t
o
=
120
s,
and the temperature at the interface is
t
o
(
30
s
)
=
24.57
°
C
after 30s of heating. A long time after the heater is deenergized,
t
≫
Δ
t
o
,
the samples reach the uniform temperature of
T
o
(
∞
)
=
33.50
°
C
.
The density of the sample materials, determined by measurement of volume and mass, is
ρ
=
3965
kg/m
3
.
Determine the specific heat and thermal conductivity of the test material. By looking at values of the thermophysical properties in Table A.1 or A.2, identify the test sample material.
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