What is the ruling on a girl refusing to cover her face due to the difficulty of doing so at university, and her unwillingness to cover it in some places but not others?

Scholars have differed on the ruling of a woman uncovering her face and hands in front of non-mahram men when there is no fear of temptation. The preponderant opinion is that it is obligatory to cover them. However, if she needs to study and cannot do so except by uncovering her face and hands, then there is no harm in her uncovering them to the extent of the need. Therefore, your friend must cover her face outside of study because she does not need to uncover it.