Question

Why is heat capacity a path function and not a state function where as temperature is a state function.

Answer 1

Any type of heat is a path function and extensive property because it depends on path followed by system like flow of heat is unidirectional in nature spontaneously as it flows from high temperatures to low temperatures.
Specific heat capacity of a substance is the heat required to raise the temperature of 1 gram of a substance by 1 degree.
Specific heat capacity is constant for a particular substance at a particular physical state and remains invariant until transition state (melting, evaporating, etc) is achieved.