Prove that in case of adiabatic lapse rate, the rate of change of air pressure with
temperature is equal to V/Cp, the terms having their usual significance
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Answer:
The temperature of the atmosphere and surface is influenced by electromagnetic radiation, and this radiation is traditionally divided into two types: insolation from the Sun and emittance from the surface and the atmosphere. Insolation is frequently referred to as shortwave radiation; it falls primarily within the ultraviolet and visible portions of the electromagnetic spectrum and consists predominantly of wavelengths of 0.39 to 0.76 micrometres (0.00002 to 0.00003 inch). Radiation emitted from Earth is called longwave radiation; it falls within the infrared portion of the spectrum and has typical wavelengths of 4 to 30 micrometres (0.0002 to 0.001 inch). Wavelengths of radiation emitted by a body depend on the temperature of the body, as specified by Planck’s radiation law. The Sun, with its surface temperature of around 6,000 kelvins (K; about 5,725 °C, or 10,337 °F), emits at a much shorter wavelength than does Earth, which has lower surface and atmospheric temperatures around 250 to 300 K (−23 to 27 °C, or −9.4 to 80.6 °F).
A fraction of the incoming shortwave radiation is absorbed by atmospheric gases, including water vapour, and warms the air directly, but in the absence of clouds most of this energy reaches the surface. The scattering of a fraction of the shortwave radiation—particularly of the shortest wavelengths by air molecules in a process called Rayleigh scattering—produces Earth’s blue skies.
When tall thick clouds are present, a large percentage (up to about 80 percent) of the insolation is reflected back into space. (The fraction of reflected shortwave radiation is called the cloud albedo.) Of the solar radiation reaching Earth’s surface, some is reflected back into the atmosphere. Values of the surface albedo range as high as 0.95 for fresh snow to 0.10 for dark, organic soils. On land, this reflection occurs entirely at the surface. In water, however, albedo depends on the angle of the Sun’s rays and the depth of the water column. If the Sun’s rays strike the water surface at an oblique angle, albedo may be higher than 0.85; if these rays are more direct, only a small portion, perhaps as low as 0.02, is reflected, while the rest of the insolation is scattered within the water column and absorbed. Shortwave radiation penetrates a volume of water to significant depths (up to several hundred metres) before the insolation is completely attenuated. The heating by solar radiation in water is distributed through a depth, which results in smaller temperature changes at the surface of the water than would occur with the same insolation over an equal area of land.
Explanation: