The specific heat of fat is 0.45 cal/(g ⋅ °C) (1.9 J/g °C) and the density of fat is 0.94 g/cm^3. How much energy (in calories and joules) is needed to heat 10 cm^3 of fat from room temperature (25 degree C) to its melting point (35 degree C)?

Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a crucial concept in thermodynamics, as it determines how much energy is needed to change the temperature of a material. In this question, the specific heat of fat (0.45 cal/(g ⋅ °C) or 1.9 J/g °C) indicates how much energy is required to heat the fat.

Density is defined as mass per unit volume and is a key property of materials. It helps in determining how much mass is contained in a given volume of a substance. In this case, the density of fat (0.94 g/cm³) allows us to calculate the mass of the fat when given its volume (10 cm³), which is essential for calculating the total energy required to heat it.

Energy calculation in thermodynamics often involves using the formula Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. This formula is fundamental for determining how much energy is needed to raise the temperature of a substance, as seen in this question where we need to calculate the energy required to heat fat from 25°C to 35°C.