A Relationship Between Skin Thermal Conductivity and Gas Polytropic Index in an Open Atmospheric Balloon

Abstract

With the assumption of a polytropic evolution for the lifting gas, the response of an ascending open atmospheric balloon to a monochromatic gravity wave is specified among other parameters by the heat balance with the surrounding air. If one considers the bubble of gas inside the open balloon as a thermodynamic system in contact through the balloon skin with a uniform thermal source (isothermic atmosphere), a relationship between the skin thermal conductivity and the polytropic index for the lifting gas [hydrogen (H2) or helium (He)] may be found. The results for both gases are extended to the case of a typical tropospheric linearly decreasing temperature profile. Constant and variable balloon skin thicknesses are studied for both background temperature profiles. The polytropic index is found to be lower for the changing skin and shows a sensitive difference between the two temperature profiles. The relationship between the thermal conductivity and polytropic index becomes abrupt only when the latter approaches the isothermal or adiabatic values.