Effective temperature of thermal radiation from non-uniform temperature distributions and nanoparticles

We study thermal radiation properties from non-uniform temperature distributions and nanoparticles, and define effective temperature. Conventionally, the temperature of a body is measured by fitting with the blackbody radiation spectrum, which assumes a uniform temperature throughout the body. We show the energy density of thermal radiation for non-uniform temperature distribution of the body and derive the effective temperature. Furthermore, the energy density of thermal radiation from nanoparticles is derived and the effective temperature of the body is shown to depend on the particle size.