A closed system has a fixed amount of matter, but it can exchange energy with the surroundings. ∆ U is measured when a closed system is used as a calorimeter because there is no change in volume and thus no expansion work can be done. An isolated system has no contact with its surroundings.

What type of system is a calorimeter?

A bomb calorimeter is a closed system because it allows heat to be exchanged. While this system is insulated, an "insulated system" is not one of the main three types of systems: closed, open, and isolated.

Is calorimeter a perfectly closed system?

The Bomb Calorimeter becomes a closed system if you don't count the surrounding environment, since there is energy flow from the rxn to the water.