Abdul Quadeer said:Homework Statement
Monochromatic energy density (Uλ)(i.e., per unit volume) of the radiation of
a blackbody is proportional to (where λ is wavelength)
(1) T4
(2) λ -5
(3) λ5/2
(4) T5/4The Attempt at a Solution
A slight modification of Stefan-Boltzmann's law suggests that the answer should be (1), but the answer given is (2). Is my book wrong?
The problem refers to " monochromatic energy density" and is thus asking about the energy density per unit wavelength.
G01 said:If you integrate that over all possible wavelengths, you get the energy density (energy/volume) which has the temperature dependence you expect.
Energy density dependence is a concept in physics that relates to the amount of energy contained in a given unit of volume. It describes how the energy of a system changes as the volume of that system changes.
Energy density dependence is typically measured by calculating the energy per unit volume of a system. This can be done by dividing the total energy of the system by its volume. Units of energy density can vary depending on the system being measured, but common units include joules per cubic meter or calories per cubic centimeter.
There are several factors that can affect energy density dependence, including the type of energy being considered (e.g. mechanical, thermal, electromagnetic), the composition of the system, and external forces acting on the system. In general, systems with higher energy densities tend to be more unstable and prone to change.
Energy density dependence has many practical applications, particularly in engineering and materials science. It is used to understand and design systems that require high energy densities, such as batteries, fuel cells, and explosives. It is also important in understanding the behavior of substances under extreme conditions, such as high temperatures and pressures.
Yes, energy density dependence can be manipulated through various means such as changing the composition of a system, applying external forces, or altering the conditions under which the system operates. This is an important factor to consider in designing and optimizing energy storage and conversion systems.