The problem of converting ambient heat into luminescence radiation is analyzed in terms of the thermodynamics of the electromagnetic field. The process is described in terms of the technical efficiency of a light source η, defined as the ratio of the power leaving the source in the form of luminescence radiation to the power supplied to the source in the form of work. For a source at the ambient temperature T, it is shown that the limitation imposed by thermodynamics is, in the steady state, η≤1+T/(Tf−T), where Tf is the ratio of the net rate at which the field carries energy away from the source to the net rate at which the field carries entropy away from the source as a result of the luminescence emission. Thus, T/(Tf−T) is the maximum possible contribution of ambient heat to the technical efficiency of a light source.
An explicit expression for Tf in terms of the ambient temperature and the spectral distribution of the luminescence emission is obtained. It is shown that Tf≥T, and that Tf is a monotonic increasing function of the ratio of the integrated intensity of the luminescence emission to the bandwidth of the emission spectrum. For moderate integrated intensities and finite (but narrow) bandwidths, it is shown that Tf is approximately equal to the brightness temperature of the light source, and it is concluded that thermodynamics forbids technical efficiencies greater than about 160% for room-temperature light sources of practical brightness. As an example, Tf is calculated for the (green) emission band of a typical ZnS phosphor.
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