Calculate the quantity of heat for copper rod whose thermal capacity is 400Jk$^{-1}$ for a temperature change of 60ºC to  80ºC

Analysis

To solve this problem, we need to understand the relationship between heat energy, thermal capacity, and temperature change.

Concept

Thermal Capacity (also known as heat capacity) is defined as the amount of heat required to raise the temperature of an object by 1 degree Celsius (or 1 Kelvin).

The formula for the quantity of heat ($Q$) is:

Where:

• $Q$ = Quantity of heat (in Joules)
• $C$ = Thermal capacity (in $J/K$ or $J/^\circ C$)
• $\Delta\theta$ = Change in temperature ($\theta_2 - \theta_1$)

Step-by-Step Solution

1. Identify the given values: • Thermal capacity ($C$) = $400 \, J/K$ • Initial temperature ($\theta_1$) = $60^\circ C$ • Final temperature ($\theta_2$) = $80^\circ C$

2. Calculate the change in temperature ($\Delta\theta$): $$\Delta\theta = 80^\circ C - 60^\circ C = 20^\circ C$$ (Note: A change of $20^\circ C$ is equivalent to a change of $20 \, K$)

3. Calculate the quantity of heat ($Q$): $$Q = 400 \, J/K \times 20 \, K$$ $$Q = 8,000 \, J$$

4. Convert to Kilojoules (KJ): Since $1,000 \, J = 1 \, KJ$: $$Q = \frac{8,000}{1,000} \, KJ = 8 \, KJ$$

Conclusion

Comparing our result to the given options, we find that $8 \, KJ$ corresponds to option D.

Exam Tip

Always watch your units! JAMB often provides answers in Kilojoules (KJ) when the calculation results in Joules (J). If you get a large number like 8,000, check if the options are in KJ by dividing by 1,000. Also, remember that a temperature change in Celsius is exactly the same as a temperature change in Kelvin, so you don't need to convert the temperatures to Kelvin before subtracting them.