Which physical quantity is not affected when temperature changes?

The question asks for the definition of specific heat capacity.

Specific heat capacity ($c$) is defined as the amount of heat energy required to raise the temperature of a unit mass of a substance by one unit of temperature (e.g., 1 Kelvin or 1 degree Celsius).

Let's evaluate the options:

• A. The amount of energy required to raise the temperature of 1 kg of the substance by 1 unit. This matches the definition: energy per unit mass (1 kg) per unit temperature change (1 unit).
• B. The amount of energy required to raise the temperature of any mass of the substance by 1 unit. This is incorrect because specific heat capacity is defined for a unit mass, not "any mass".
• C. The amount of energy required to change the state of 1 kg of the substance without changing its temperature. This describes specific latent heat, not specific heat capacity. Specific heat capacity involves a temperature change.
• D. The amount of energy required to change the state of any mass of the substance without changing its temperature. This is also related to latent heat and is incorrect for the same reasons as B and C.

Therefore, option A is the correct definition.

The final answer is $\boxed{\text{A}}$