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The specific heat of a material is defined as the amount of energy required to raise the temperature of a unit mass of that material by one degree Celsius (or one Kelvin). Therefore, measuring the energy absorbed per unit mass per degree temperature rise directly corresponds to this definition. This measurement provides vital information about how a material responds thermally, which is essential in various applications, from engineering to material science.

The other choices do not accurately reflect the concept of specific heat. For example, measuring volume absorbed per unit mass does not relate to thermal energy but rather to the physical characteristics of a substance, and changes in material density would not convey the same thermal energy information. Similarly, the weight of the material before heating does not provide insights into how effectively the material can store heat as it does not take into account the energy changes involved in temperature variation. Thus, the focus on energy absorption per unit mass per degree rise is critical for understanding specific heat.