One end of a solid cylindrical copper rod 0.1500 m long and 0.0250 m in radius is inserted into a large block of solid hydrogen at its melting temperature, 13.84 K. The other end is blackened and exposed to thermal radiation from surrounding walls at 550.0 K. (Some telescopes in space employ a similar setup. A solid refrigerant keeps the telescope very cold-required for proper operation- even though it is exposed to direct sunlight.) The sides of the rod are insulated, so no energy is lost or gained except at the ends of the rod. See the sketch in (Figure 1 ) (a) When equilibrium is reached, what is the temperature of the blackened end? The thermal conductivity of copper at temperatures near 20 K is 1670 W/m. K. (b) At what rate (in kg/h) does the solid hydrogen melt? Figure Solid hydrogen, Hyd T-13.84 K Tc 2R Copper cylinder L < 1 of 1 www.Ts Part G Solve for the temperature of the blackened end of the rod. Express your answer in kelvins. ► View Available Hint(s) THot 14.31 K = Submit Previous Answers ✓ Correct Part H Use your result from the previous part to find the rate at which the hydrogen melts. Express your answer in kilograms per hour. ► View Available Hint(s) |Π| ΑΣΦ dmHyd/dt = 14.49 O www p ? kg/h Review | Constants.

Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter21: Heat And The First Law Of Thermodynamics
Section: Chapter Questions
Problem 61PQ
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Please answer part H

One end of a solid cylindrical copper rod 0.1500 m long
and 0.0250 m in radius is inserted into a large block of
solid hydrogen at its melting temperature, 13.84 K. The
other end is blackened and exposed to thermal radiation
from surrounding walls at 550.0 K. (Some telescopes in
space employ a similar setup. A solid refrigerant keeps
the telescope very cold-required for proper operation-
even though it is exposed to direct sunlight.) The sides of
the rod are insulated, so no energy is lost or gained
except at the ends of the rod. See the sketch in (Figure 1
)
(a) When equilibrium is reached, what is the temperature
of the blackened end? The thermal conductivity of copper
at temperatures near 20 K is 1670 W/m.K. (b) At
what rate (in kg/h) does the solid hydrogen melt?
Figure
Solid hydrogen, m Hyd
THyd 13.84 K
Tc
2R
Copper cylinder
L
1 of 1
www.Ts
TH
Part G
Solve for the temperature of the blackened end of the rod.
Express your answer in kelvins.
► View Available Hint(s)
THot
Submit
14.31 K
Part H
Previous Answers
Correct
Use your result from the previous part to find the rate at which the hydrogen melts.
Express your answer in kilograms per hour.
► View Available Hint(s)
IVE ΑΣΦ
dmHyd/dt = 14.49
M
?
kg/h
Review | Constants
Transcribed Image Text:One end of a solid cylindrical copper rod 0.1500 m long and 0.0250 m in radius is inserted into a large block of solid hydrogen at its melting temperature, 13.84 K. The other end is blackened and exposed to thermal radiation from surrounding walls at 550.0 K. (Some telescopes in space employ a similar setup. A solid refrigerant keeps the telescope very cold-required for proper operation- even though it is exposed to direct sunlight.) The sides of the rod are insulated, so no energy is lost or gained except at the ends of the rod. See the sketch in (Figure 1 ) (a) When equilibrium is reached, what is the temperature of the blackened end? The thermal conductivity of copper at temperatures near 20 K is 1670 W/m.K. (b) At what rate (in kg/h) does the solid hydrogen melt? Figure Solid hydrogen, m Hyd THyd 13.84 K Tc 2R Copper cylinder L 1 of 1 www.Ts TH Part G Solve for the temperature of the blackened end of the rod. Express your answer in kelvins. ► View Available Hint(s) THot Submit 14.31 K Part H Previous Answers Correct Use your result from the previous part to find the rate at which the hydrogen melts. Express your answer in kilograms per hour. ► View Available Hint(s) IVE ΑΣΦ dmHyd/dt = 14.49 M ? kg/h Review | Constants
Expert Solution
Step 1

We have, radius (r) = 0.025 m

Length (L) = 0.15 m

Thermal conductivity of copper (k) = 1670 W/m.k

Latent heat of fusion of copper (Lf) = 206 KJ/kg

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