The interrelationship between the mechanical work done on a material in the elastic range and changes in its thermodynamic properties, that is, between stress and strain, on the one hand, and temperature and entropy, on the other, is known as the thermoelastic effect. The phenomenon is exactly adiabatic and is characterized by the thermoelastic quotient commonly referred to as thermoelastic constant. The thermoelastic effect can be used for stress analysis by monitoring the stress fluctuations by means of infrared radiometry. Also, it can be applied to study the anharmonicity in materials by measuring the temperature changes associated with adiabatic pressure changes. In this paper thermodynamic expressions are derived for the pressure derivative of the thermoelastic quotient under adiabatic as well as isothermal conditions. The derived expressions are applied to investigate the thermoelastic effect for the three glasses, namely, silica glass, soda-lime silica glass, and lead-silica glass. The isothermal pressure derivative of the thermoelastic quotient is evaluated for the three glasses. The isothermal volume derivative of the Gruneisen function is calculated.