The Evaporating Droplet Engine · AI Generator #GEN-7D2A8611
Physics · thermodynamics
Problem
A brilliant engineer proposes a novel micro-engine that operates by the controlled evaporation of water droplets. The engine consists of a small chamber containing a spherical water droplet of initial radius R0=2.0mm at temperature T=373K. The chamber has rigid walls and initial volume V0=1.0cm3.
The droplet evaporates completely, and the resulting water vapor behaves as an ideal gas. The vapor then undergoes an adiabatic expansion as a piston moves outward, allowing the gas to do work. During this expansion, the volume increases by a factor of 8.
For water vapor, assume γ=1.33 and molar mass M=18.0g/mol. The density of liquid water is ρ=1000kg/m3. Assume the evaporation occurs at constant volume and the vapor reaches thermal equilibrium at 373K before expansion begins.
(a) Find the pressure of the water vapor just after complete evaporation but before expansion begins.
(b) Calculate the work done by the gas during the subsequent adiabatic expansion.