Since egg shell is made of calcium carbonate. And we know that when calcium carbonate (CaCO3) reacts with nitric acid (HNO3) then carbon dioxide, calcium nitrate and water are formed. So same reaction happens when nitric acid is added to an eggshell.
Chemical equation for reaction of nitric acid with egg shell :-
CaCO3 + 2HNO3→ Ca(NO3)2 + CO2 + H2O
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