Approximately how much thermal energy is needed to raise the temperature of this sample of glycerin to 75 °C?

Question

A soap maker needs to melt a 13-kilogram slab of glycerin so that it can then be poured into soap molds.  The glycerin is at 23 °C and needs to be heated to 75 °C. Glycerin has a specific heat of 2400 J/kg•K.

Answer 1

We know the specific heat, c, of glycerin is 2400 J/kg*K. Start by calculating heat capacity of our sample:

Heat capacity = c * m = 13 kg * 2400 J/kg*K = 31,200 J/K

Thus, 31,200 J of energy are required to raise the temperature of this glycerin sample by one degree. Now, calculate the temperature change:

We could convert to Kelvin, but because we are adding the same number (273), to both temperatures, and finding the difference, we can just find the difference between temperatures in Celsius, i.e. 75-23 = 52.

Thus, the total energy:

52 K *31,200 J/K = 1622400 J = 1622.4 kJ