Specific Heat Capacity (DP IB Physics: SL)

• The amount of thermal energy needed to change the temperature of an object depends on:
  • The change in temperature required ΔT - i.e. the larger the change in temperature the more energy is needed
  • The mass of the object m - i.e. the greater the mass the more energy is needed
  • The specific heat capacity c of the given substance - i.e. the higher the specific heat capacity the more energy is needed

• The equation for the thermal energy transferred, Q, is then given by:

Q = mcΔT

• Where:
  • m = mass of the substance in kilograms (kg)
  • ΔT = change in temperature in kelvin (K) or degrees Celsius (°C)
  • c = specific heat capacity of the substance (J kg^–1 K^–1)

• The specific heat capacity of a substance is defined as:

The amount of energy required to change the temperature of 1 kg of a substance by 1 K (or 1°C)

• This definition can be explained when the above equation is rearranged for c:

• This means that, the higher the specific heat capacity of a substance the longer it takes for the substance to warm up or cool down
  • Note that the specific heat capacity is measured in J kg^–1 K^–1

Step 1: Write down the known quantities 

• • Mass of copper = 2 kg
  • Mass of water = 5 L = 5 kg
  • Initial temperature of copper = –10°C
  • Initial temperature of water = 20°C
  • Final temperature of water = 18°C
  • Change in temperature of water = 18°C – 20°C = –2°C
  • Specific heat capacity of water = 4200 J kg^–1 K^–1
  • Specific heat capacity of copper = 390 J kg^–1 K^–1

Step 2: Write down the equation for thermal energy 

Q = mcΔT

Step 3: Determine the energy transferred from the water to the copper

• • The water is at a higher temperature than copper, hence thermal energy will flow from the water to the copper
  • To quantify this energy, substitute numbers into the above equation
  • In this case, the mass m is that of the water
  • The specific heat capacity is that of water
  • Since this is the energy lost by the water, it will be negative

Q = 5 kg × 4200 J kg^–1 K^–1 × (–2°C) = – 42000 J

Step 3: Determine the change in temperature ΔT of the copper 

• • The energy lost by the water is the same as the energy gained by the copper
  • Since this is the energy gained by the copper, it is positive
  • The equation for thermal energy can be rearranged to calculate the change in temperature ΔT of the copper
  • In this case, the mass m is that of the copper
  • The specific heat capacity is that of copper

• 

Step 4: Determine the final temperature of the copper

• • Since the copper gains thermal energy, its final temperature will be higher than its initial temperature

final temperature of copper = ΔT + initial temperature of copper = 54°C – 10°C

final temperature of copper = 44°C