For a bomb calorimeter, which thermodynamic quantity is directly measured?
A bomb calorimeter operates at constant volume, so Δ U = q_v is measured. This follows from NCERT principle where relation explains outcome clearly for students.
Ref: NCERT Chemistry Textbook for Class XI and XII, Chapter: Some Basic Concepts, Structure of Atom, Periodicity and relevant Chemistry topic, Topic: Mole concept and periodic trends.