The present invention provides an improved valve. This valve opens and closes in response to a change in the physical environment of the valve. This valve is particularly suited as a relief valve in a microwave system-based, closed vessel digestion procedure. This valve includes a pressure-deformable, resilient wall member having a fluid vent port, and an obstructing member that cooperates with the wall member to open and close the valve. Also provided is a lidded vessel employing this improved valve, an apparatus that includes a microwave system and this lidded vessel, and methods using this improved valve.