I got stuck on the following problem, which is very important for my exam preparations - would anyone mind giving me a hint? A ballon of Volume V(0) is tethered to the ground using a light cable. It is filled with helium gas of density rho (He). At ground level the pressure and density in the atmosphere are p(0) and rho(0) respectively. The atmosphere is isothermal with a temperature T(0). The balloon is allowed to rise to a height h by very slowly letting out the cable. At all heights the gas pressure inside the balloon equals the pressure outside. I have already shown that for the pressure and density the following is true: [tex] p/p_0 = exp(-mgh/kT) = \rho/\rho_0 [/tex] QUESTION: The He in the balloon (an excellent insulator) expands adiabatically. What is the pressure in the balloon at height h and find its volume. Please, please, can anyone give me a hint ?