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The electrode-gap effects on discharge characteristics have attracted increasing attention in the design of atmospheric discharge devices. In this paper, a 1-D fluid model is used to explore the influences of electrode gap on the electron density and temperature of atmospheric radio-frequency discharges under a constant power density condition. As the electrode gap is increased, both the applied voltage and current density increase and the computational data and analytical equations show a monotonic increase in the electron density; the peak electron temperature in the sheath increases but decreases in the bulk plasma region. At a constant power density, altering the electrode gap can be used to tailor the spatial distribution of the electron density and electrode temperature.