Temperature change and heat transfer
Equal heat transfers can produce different temperature changes in different materials or sample sizes. Heat capacity quantifies this response, commonly in joules per kelvin. Temperature describes a system’s state, while heat is energy transferred because of a temperature difference, so the two quantities play different roles.
References: [1]
Normalizing the comparison
Total heat capacity changes with the amount of material. Specific heat capacity normalizes by mass and molar heat capacity by amount of substance. Treating either as constant requires a suitable temperature range; a substance can respond differently at another temperature or in another physical phase.
Constant pressure and constant volume
A heated gas may expand and perform work, so equal temperature rises require different heat transfers at constant pressure and constant volume. The ideal-gas model gives a definite relationship between these molar capacities. Specifying the process links heat-capacity measurements to the first law of thermodynamics.
References: [2]
Calorimetry and phase changes
Calorimetry balances transferred and retained energy to infer thermal properties. During a phase change such as melting, added energy can change the phase while temperature remains approximately constant. Latent-heat descriptions handle this behaviour, extending beyond a single constant-heat-capacity expression applied over the whole heating process.
References: [1]