Specific Heat Capacity (DP IB Physics)

A piece of copper of mass 50 g is heated until it reaches a temperature of 120 °C. The copper is removed from the heat and immediately placed into 250 mL of water at 25 °C.

The temperature of the water and copper is measured until they reach thermal equilibrium.

Determine the final temperature of the copper and water, in degrees Celsius (°C), assuming no heat is lost to the surroundings.

• The specific heat capacity of water is 4200 J kg^–1 K^–1

• The specific heat capacity of copper is 390 J kg^–1 K^–1

Answer:

Step 1: Write down the known quantities 

• Mass of copper, m_c = 50 g = 0.05 kg

• Mass of water, m_w = 250 ml = 0.25 kg (since 1 litre = 1 kg)

• Initial temperature of copper, T_c = 120 °C

• Initial temperature of water, T_w = 25°C

• Specific heat capacity of water, c_w = 4200 J kg^–1 K^–1

• Specific heat capacity of copper, c_c = 390 J kg^–1 K^–1

Step 2: Write down the equation for thermal energy 

Step 3: Equate the equations for the energy transferred from the copper to the water

• The copper is at a higher initial temperature than the water, hence thermal energy will be transferred from the copper to the water

• The energy lost by the copper = the energy gained by the water

Step 4: Determine the final temperature T_f of the copper and water

• Since the water and copper reach thermal equilibrium, their final temperature T_f will be the same

You should notice that changes in temperature ΔT can usually be written in degrees Celsius (although this is not the SI base unit for temperature) and do not need to be converted into kelvin (K). This is because differences in absolute temperatures always correspond to differences in Celsius temperature.

If the question asks to determine the initial or final temperature of a substance, make sure you always check the unit of measure (°C or K) in which you are required to give your final answer.