For an ideal radiator (hohlraum) with a 10-cm-diameter opening, located in black surroundings at 16°C, (a) calculate the net radiant heat transfer rate for hohlraum temperatures of 100°C and 560°C, (b) the wavelength at which the emission is a maximum, (c) the monochromatic emission at ?max, and (d) the wavelengths at which the monochromatic emission is 1 per cent of the maximum value.
GIVEN
• An ideal radiator (hohlraum) in black surroundings
• Radiator opening diameter (D) = 10 cm = 0.1 m
• Surrounding temperature (Ts) = 16°C = 289 K
• Hohlraum temperatures
- Th1 = 100°C = 373 K
- Th2 = 560°C = 833 K
FIND
(a) The net radiant heat transfer rate (qr)
(b) The wavelength at which the emission is maximum (?max)
(c) The monochromatic emission at ? max (E?max)
(d) The wavelengths at which the monochromatic emission is 1% E?max
SKETCH
PROPERTIES AND CONSTANTS
the Stephan-Boltzmann constant (?) = 5.67 × 10–8 W/(m2 K4)
All parts of the problem will first be solved for Th = 373 K
(a) The net radiative transfer between any two black surfaces is
(b) The wavelength at which the maximum emission occurs for a black body is
(c) The monochromatic emission is
(d)
(There will be one solution below ?max and one above ?max)
By trial and error
Repeating the above proceduur for Th = 833 K
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A long copper cylinder 0.6-m in diameter and initially at a uniform temperature of 38°C is placed in a water bath at 93°C. Assuming that the heat transfer coefficient between the copper and the water is 1248 W/(m2 K), calculate the time required to heat the center of the cylinder to 66°C. As a first approximation, neglect the temperature gradient within the cylinder, then repeat your calculation without this simplifying assumption and compare your results.
GIVEN
• A long copper cylinder is placed in a water bath
• Diameter of cylinder (D) = 0.6 m
• Initial temperature (To) = 38°C
• Water bath temperature (T?) = 93°C
• The heat transfer coefficient ( ) ch = 1248 W/(m2 K)
FIND
Calculate the time required to heat the center of the cylinder to 66°C assuming
(a) Negligible temperature gradient within the cylinder
(b) Without this simplification, then
(c) Compare your results
ASSUMPTIONS
• Neglect end effects
• Radial conduction only
SKETCH
When an electron is removed from a neutral atom, it becomes
A) a positive ion. B) a negative ion. C) heavier. D) a bipolar atom. E) more massive.
The length of a certain wire is halved while the radius is doubled. What is the change in the resistance of this wire?
A) It stays the same. B) It is reduced by a factor of 2. C) It is reduced by a factor of 4. D) It is reduced by a factor of 8. E) It is quadrupled.
If the radiant energy from the sun comes in as a plane EM wave of intensity 1 340 W/m2, calculate the peak values of E and B
a. 300 V/m, 10-4 T b. 1 000 V/m, 3.35 × 10^-6 T c. 225 V/m, 1.60× 10-3 T d. 111 V/m, 3.00 × 10^-5 T e. 711 V/m, 2.37 × 10^-6 T