What does it mean by exchange of matter? 
What does it mean by exchange of matter and energy means here?
 A: By exchange of matter , it is referring to the fact that free molecules can move freely and can move inside or outside the system.
For example , suppose you take a balloon and inflate it through your mouth . Now , if you leave the mouth of the balloon free, you notice that the air inside the balloon comes out of the balloon . This is what called exchange of matter.
And by exchange of energy , it means that energy can flow inside or outside the system through temperature difference or other methods like the high energy molecules can go out of the system and thus the system will lose its energy.
Hope it helps .
A: Consider a simple example of the Human body. You, like all living things, are an open system, meaning that you exchange both matter and energy with your environment. For instance, you take in chemical energy in the form of food, and do work on your surroundings in the form of moving, talking, walking, and breathing.
In your example, As the beaker is open so reactant can be exchange from surrounding; for example, you are boiling water in open beaker then water vapour can flow outside. That mean it can exchange matter from outside. Now beaker is made up of thermal conducting material so you can heat up the beaker so there is a exchange of energy from surrounding.
Let's sum up; If the mass of the system is not conserved that mean that there is a exchange of matter. If the energy of the system is not conserved that mean there is a exchange of energy.
