What is the relationship between the wavelength of a wave and it's energy?

In general, the energy of a wave is inversely proportional to its wavelength.

Explanation:

Start with the simple proportional relationship: Energy of a wave is directly proportional to the wave's frequency. In quantum physics, the constant of proportionality is the Planck's constant . Symbolically, for a photon (elementary unit of electromagnetic waves)

Frequency f, on the other hand, is inversely proportional to the wavelength . The constant here is the propagation speed v:

and so combining both relationships, we get the following relationship between the energy and the wavelength:

In classical physics, energy is jointly proportional to the square of the amplitude and to its frequency. Again, this implies an inversely proportional relationship to its wavelength.

In summary, the energy of a wave is inversely proportional to its wavelength.

answer: 802.3 kilo joules of energy represents 191.75 kilo calorie of energy.

explanation:

energy released during combustion of one mole methane = 802.3 kilo joules

if 1 kilo joule = 0.239006   kilo calorie

then ,802.3 kilo joule will be = 802.30.239006 kilo calorie

802.3 kilo joule = 191.75 kilo calorie

hence, the energy in kilo calorie is 191.75 kilo calorie.

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

-it's clean and sustainable

-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

-almost everywhere, the shallow ground or upper 10 feet of the earth's surface maintains a nearly constant temperature between 50° and 60°f (10° and 16°c)

-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

-in the winter, the heat pump removes heat from the heat exchanger and pumps it into the indoor air delivery system

-in the summer, the process is reversed, and the heat pump moves heat from the indoor air into the heat exchanger

-the heat removed from the indoor air during the summer can also be used to provide a free source of hot water