A zinc has a heat capacity of 40 J/K, what is the mass of the zinc, given that the specific heat of zinc is 380 J/kg k

Analysis

To solve this problem, we need to understand the relationship between Heat Capacity and Specific Heat Capacity.

• Heat Capacity ($C$): The amount of heat required to raise the temperature of the entire body by 1 Kelvin. Its unit is $J/K$.
• Specific Heat Capacity ($c$): The amount of heat required to raise the temperature of unit mass (1kg) of a substance by 1 Kelvin. Its unit is $J/kg \cdot K$.

Concept

The formula connecting these two is:

Where:

• $C$ = Heat Capacity ($40 \, J/K$)
• $m$ = Mass ($kg$)
• $c$ = Specific Heat Capacity ($380 \, J/kg \cdot K$)

Solution

1. Rearrange the formula to solve for mass ($m$): $$m = \frac{C}{c}$$

2. Substitute the given values into the equation: $$m = \frac{40}{380}$$

3. Calculate the result: $$m = \frac{4}{38}$$ $$m \approx 0.10526... \, kg$$

4. Rounding: Rounding $0.10526$ to two decimal places gives us $0.11 \, kg$.

Conclusion

Comparing our result to the provided options, $0.11 \, kg$ matches option A.

Exam Tip

Always check your units before calculating! If the specific heat capacity were given in $J/g \cdot K$ instead of $J/kg \cdot K$, you would have had to convert the mass units accordingly. In JAMB Physics, always ensure your mass is in kilograms (kg) when working with standard SI units.