Attempt : 1. Pressure at height ##z## : ##P(z) = P_{\text{atm}}-\rho_0 gz ##, ignoring density variation. But actually, we have ##\rho(z)<\rho_0\;\forall z>0##. Hence, we are subtracting a bigger value from ##P_{\text{atm}}## than we actually should, meaning that we would end up what a smaller...