The history of the discovery of hot gas in galaxies is briefly reviewed, and the main properties of this gas described, emphasizing the need to refine these properties, in particular, the mass of the gas. It is proposed to do this via observations of the Sunyaev-Zel'dovich (SZ) effect due to hot gas in the coronas of elliptical galaxies. The absolute and relative perturbations of the spectrum of the cosmic microwave background (CMB) radiation due to scattering of the CMB photons by electrons with a Maxwellian energy distribution are calculated. The possibility of observing the SZ effect is demonstrated using three elliptical galaxies as examples. The kinematic SZ effect arising due to the peculiar motions and rotations of the galaxies is also accessible to observations. Together with X-ray data, such observations would enable refinement of the properties of gas in galaxies, and also yield additional information about the rotation of galaxies, possible accretion flows in the galactic gas, and hot galactic winds. © 2008 Pleiades Publishing, Ltd.