on aircraft carriers, catapults are used to accelerate jet air craft to flight speeds in a short distance. One such catapult tak
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Answer:
a) -0.0934 kJ/kg. K
b) The direction of flow is from right to left.
Explanation:
A free flow diagram of the horizontal insulated duct is as shown below.
NOW,
Let assume that the direction of flow is from left to right and consider the following relation for the entropy rate balance equation for a control volume as:
Now; if the value for this relation is greater than zero; then we conclude that our assumption is correct.
If the value is less than zero; then we conclude that the assumption is wrong.
Then, the flow is said to be in the opposite direction
Formula for the change in specific entropy can be calculated as:
where;
are specific entropies
R = universal gas constant
= pressure at location 1
= pressure at location 2
We obtain the specific properties of air at temperature at = (67°C + 273)K = 340 K from the table A-22 ( Ideal gas properties of air)
= 1.8279 kJ/kg.K
We also obtain the specific properties of air at temperature = 22°C + 273) K = 295 K
From the table A- 22
= 1.68515 kJ/kg . K
R =
0.95 bar
0.8 bar
Now replacing our values into equation (2) from above; we have;
Equating our result to equation (1)
Therefore , our assumption is wrong and the direction of flow is said to be from right to left.
We therefore conclude that the direction of flow is from right to left.
Answer:
a) What are the characteristics of the radiation emitted by a blackbody?
The total emitted energy per unit of time and per unit of area depends in its temperature (Stefan-Boltzmann law).
The peak of emission for the spectrum will be displaced to shorter wavelengths as the temperature increase (Wien’s displacement law).
The spectral density energy is related with the temperature and the wavelength (Planck’s law).
b) According to Wien's Law, how many times hotter is an object whose blackbody emission spectrum peaks in the blue, at a wave length of 450 nm, than a object whose spectrum peaks in the red, at 700 nm?
The object with the blackbody emission spectrum peak in the blue is 1.55 times hotter than the object with the blackbody emission spectrum peak in the red.
Explanation:
A blackbody is an ideal body that absorbs all the thermal radiation that hits its surface, thus becoming an excellent emitter, as these bodies express themselves without light radiation, and therefore they look black.
The radiation of a blackbody depends only on its temperature, thus being independent of its shape, material and internal constitution.
If it is study the behavior of the total energy emitted from a blackbody at different temperatures, it can be seen how as the temperature increases the energy will also increase, this energy emitted by the blackbody is known as spectral radiance and the result of the behavior described previously is Stefan's law:
(1)
Where is the Stefan-Boltzmann constant and T is the temperature.
The Wien’s displacement law establish how the peak of emission of the spectrum will be displace to shorter wavelengths as the temperature increase (inversely proportional):
(2)
Planck’s law relate the temperature with the spectral energy density (shape) of the spectrum:
(3)
b) According to Wien's Law, how many times hotter is an object whose blackbody emission spectrum peaks in the blue, at a wavelength of 450 nm, than a object whose spectrum peaks in the red, at 700 nm?
It is need it to known the temperature of both objects before doing the comparison. That can be done by means of the Wien’s displacement law.
Equation (2) can be rewrite in terms of T:
(4)
Case for the object with the blackbody emission spectrum peak in the blue:
Before replacing all the values in equation (4), (450 nm) will be express in meters:
⇒
Case for the object with the blackbody emission spectrum peak in the red:
Following the same approach above:
⇒
Comparison:
The object with the blackbody emission spectrum peak in the blue is 1.55 times hotter than the object with the blackbody emission spectrum peak in the red.