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The James Webb Space Telescope's Medium Resolution Spectrometer (MRS), willoffer nearly 2 orders of magnitude improvement in sensitivity and >3Ximprovement in spectral resolution over our previous space-based mid-IRspectrometer, the Spitzer IRS. In this paper, we make predictions forspectroscopic pointed observations and serendipitous detections with the MRS.Specifically, pointed observations of Herschel sources require only a fewminutes on source integration for detections of several star-forming and activegalactic nucleus lines, out to z$=$3 and beyond. But the same data will alsoinclude tens of serendipitous 0$\lesssim$z$\lesssim$4 galaxies per field withinfrared luminosities ranging $\sim10^6-10^{13}$L$_{\odot}$. In particular, forthe first time and for free we will be able to explore the$L_{IR}<10^{9}L_{\odot}$ regime out to $z\sim3$. We estimate that with$\sim$100 such fields, statistics of these detections will be sufficient toconstrain the evolution of the low-$L$ end of the infrared luminosity function,and hence the star formation rate function. The above conclusions hold for awide range in potential low-$L$ end of the IR luminosity function, andaccounting for the PAH deficit in low-$L$, low-metallicity galaxies.

Exploring the evolution of star formation and dwarf galaxy properties with JWST/MIRI serendipitous spectroscopic surveys