The method for determining energy expenditure that involves the measurement of heat given off by the body during a select period of time in an insulated chamber is

The correct answer is direct calorimetry.

Explanation:

A method of attaining direct determination of the concentration of heat produced by the body inside an insulated chamber, which is sufficiently big to allow moderate amounts of work is termed as direct calorimetry. These chambers within which the measurement is done is also known as the whole-room calorimeters.  

The mentioned process provides the measurement of the energy discharged in the form of heat.