No they cannot be negative. Heat capacity is how much energy has to be gained to raise a substance's temperature by a certain amount. This is endothermic and therefore must be positive.

What does a negative specific enthalpy mean?

A negative enthalpy represents an exothermic reaction, releasing heat. A reaction that absorbs heat is endothermic. Its enthalpy will be positive, and it will cool down its surroundings.

Can change in specific enthalpy be negative?

For this reason, the change in enthalpy, ΔH , for an exothermic reaction will always be negative. ... Exothermic reaction: In an exothermic reaction, the total energy of the products is less than the total energy of the reactants. Therefore, the change in enthalpy is negative, and heat is released to the surroundings.