Calculate the heat capacity of a material that absorbs 48KJ of heat at a differential temperature of 53ºC

1. Analyze the question

We are asked to find the heat capacity ($C$) of a material. We are given:

• Heat absorbed ($Q$) = $48\text{ kJ} = 48,000\text{ J}$
• Temperature change ($\Delta\theta$ or $\Delta T$) = $53^\circ\text{C}$ (Note: A change in Celsius is equivalent to a change in Kelvin, so $\Delta T = 53\text{ K}$)

2. Explain the concept

Heat Capacity ($C$) is defined as the amount of heat required to raise the temperature of an entire object by one degree Celsius (or one Kelvin). It is different from Specific Heat Capacity (which is per unit mass).

The formula is:

Where:

• $C$ is the heat capacity in $\text{J/K}$ (or $\text{J/}^\circ\text{C}$)
• $Q$ is the quantity of heat in Joules ($\text{J}$)
• $\Delta T$ is the change in temperature in Kelvin ($\text{K}$) or Celsius ($^\circ\text{C}$)

3. Show the solution

• Step 1: Convert the heat from kilojoules to Joules. $$48\text{ kJ} = 48 \times 1,000 = 48,000\text{ J}$$

• Step 2: Apply the formula. $$C = \frac{48,000\text{ J}}{53\text{ K}}$$

• Step 3: Perform the division. $$C \approx 905.660377\dots\text{ J/K}$$

• Step 4: Round to one decimal place as per the options provided. $$C \approx 905.7\text{ J/K}$$

4. Identify the answer

Comparing our result to the given options, $905.7\text{ JK}^{-1}$ matches option C.

5. Exam Tip

Always watch your units! JAMB often provides heat in kilojoules (kJ) while the options are in Joules (J). Always convert to the base unit (Joules) before dividing to avoid common calculation errors. Also, remember that a change of $1^\circ\text{C}$ is exactly the same as a change of $1\text{ K}$, so you don't need to add $273$ to the temperature change.