After the Duke of Devonshire banished Georgiana to the continent for her affair with Charles Grey, the active Duchess was left without her children to tend to, London to party in, or politics to involve herself in. She was left to deal with her grief in foreign lands, but luckily, alongside her mother, sister, and an ever-growing entourage. Oh yeah, Bess was there too.
After dealing with the many agonizing emotions of her predicament, Georgiana had to find other things to involve herself in while she was abroad. At first this consisted of the usual English-travelers abroad regime: visit Grand Tour stops, stay with ex-expatriates living abroad, etc, etc. But then Georgiana began actually getting inspired by her visits with expatriates, notably the scientists. Georgiana attempted to better herself with studies of all sorts, but it was chemistry and mineralogy that she became the most interested in. The famous Chemist, Charles Blagden encouraged and motivated Georgiana in her studies. Blagden is given credit for his research in persipitation freezing points in liquid. The two would remain friends for the rest of Georgiana's life.
Instead of political circles and debates it was now scientific circles and lectures. Instead of being a patroness of young actors, as she was in her premiere duchess years, she was now funding scientists. Her return from exile didn't diminish Georgiana's new found interest. She set up a mini lab in Devonshire House to conduct experiments and blessed Chatsworth with one of the finest fossil and mineral collections, which it has to this day. Her new interest also brought her closer to her husband's shy uncle, Henry Cavendish, who discovered Hydrogen. Georgiana couldn't get enough science, and perhaps, if she was born in a different era more open to educated women in this field, she could have made a significant impact on the scientific world.