By using the ideal gas law and the provided data on Pluto's atmospheric density and pressure, we estimate the temperature of Pluto's atmosphere to range between 50 K and 60 K, making simplifying assumptions about the thinness of the atmosphere and weak solar radiation.
To estimate the temperature of Pluto's atmosphere, we need to use the provided information about atmospheric pressure and density changes with altitude. The ideal gas law is a good starting point, which is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Assuming the atmosphere behaves like an ideal gas and considering the conditions given, we know that the density at 50 km is one-third of the surface density, and Pluto's atmosphere has a pressure about a ten-thousandth of Earth's when the planet is closest to the Sun. Given the pressure and density relationship with temperature in the ideal gas law, atmosphere pressure, and surface temperature are related.
We can make a simplifying assumption that the atmospheric temperature at the surface will not differ significantly from the average surface temperature ranges provided (50 K to 60 K) because of the thin atmosphere and weak solar radiation at the distance of Pluto from the Sun. Considering these, we can estimate that the temperature of Pluto's atmosphere close to the surface will also be in the range of 50 K to 60 K.
We have made some simplifying assumptions, such as ignoring the layered structure of the atmosphere indicated by the haze layers and neglecting any potential heat sources other than the Sun. We are also ignoring the heat capacity and thermal conductivity of atmospheric gases.