Specific Heat Capacity The use of an equation CHAPTER 15

Definition If 1 kg of water and 1 kg of paraffin are heated in turn for the same time by the same heater, the temperature rise of the paraffin is about twice that of the water. Since the heater gives equal amounts of heat energy to each liquid, it seems that different substances require different amounts of heat to cause the same temperature rise in the same mass, say 1 o C in 1 kg.

Definition The ‘thirst’ of a substance for heat is measured by its specific heat capacity (symbol c). The specific heat capacity of a substance is the heat required to produce unit temperature rise in unit mass

Definition Heat, like other forms of energy, is measured in Joules (J) and the unit of specific heat capacity is the joule per kilogram degree Celsius. i.e.Unit of c = J/kg o CorJkg -1 o C -1 In physics the word ‘specific’ means ‘unit mass’ is being considered.

The heat equation If a substance has a specific heat capacity of 1000 J/kg o C then 1000J raise the temp. of 1kg by 1 o C 2 × 1000J raise the temp. of 2kg by 1 o C 3 × 2 × 1000J raise the temp. of 2kg by 3 o C That is, 6000J will raise the temperature of 2kg of this substance by 3 o C.

The heat equation We have obtained this answer by multiplying together: (i)The mass in kg (ii)The temperature rise in o C, and (iii)The specific heat capacity in J/kg o C If the temperature of the substance fell by 3 o C, the heat given out would also be 6000J.

The heat equation In general, we can write the ‘heat equation’ as i.e. E = mc  T Heat received or given out =mass × Temp. Change × Specific Heat Capacity

Table 1 The following table gives the specific heat capacity of some common substances. SubstanceSpecific heat capacity c ( J kg -1 o C -1 ) Water4200 Alcohol2400 Sand840 Granite800 Ice2100 Glass670 Copper390 Iron460

Example Find the heat received, if the temperature of a 5kg mass of copper of specific heat capacity 400 J/kg o C rises from 15 o C to 25 o C. Answer E = mc  T E = 5 kg × 400 J/kg o C × (25 – 15) o C E = 5 × 10 × 400 = J

Exercise 1 1)Find the heat received, if the temperature of a 15kg mass of aluminium of specific heat capacity 900 J/kg o C rises from -12 o C to 22 o C. 2)How much heat is needed to raise the temperature by 10 o C of 5kg of a substance of specific heat capacity 300 J/kg o C?