Q. A) Imagine a tall vertical column of gaseous or liquid fluid whose density varies with height. Show that the pressure as a function of height follows the differential equation . B) Solve this differential equation for the case of a gaseous atmosphere of molecular weight , in which the temperature is constant as a function of . A. A) Imagine the volume of unit area and infinitesimal height . Number of molecules = At equilibrium the force of gravity in the volume plus pressure difference is zero. , where is mass of one molecule. For unit mass B) For ideal gas , where is number of molecules in volume . Then, for unit volume , where is number of molecules in unit volume, which means density. From eq.(1) We need . Substituting to eq.(2) gives , where . Reference molecule weight Avogadro constant
Comments
Post a Comment