Calculate the specific heat capacity of a metal rod of mass 0.025kg whose temperature was raised by 15ºC when…

Analysis

To solve this problem, we need to relate the heat energy supplied to a substance with the resulting change in its temperature. This is a classic calorimetry problem involving the specific heat capacity formula.

Concept

The formula for heat energy ($Q$) is given by:

Where:

• $Q$ = Heat energy supplied (in Joules, J)
• $m$ = Mass of the substance (in kilograms, kg)
• $c$ = Specific heat capacity (in Jkg$^{-1}$K$^{-1}$)
• $\Delta\theta$ = Change in temperature (in Kelvin or Celsius, as the interval is the same)

We need to rearrange this formula to solve for the specific heat capacity ($c$):

Solution

Step 1: Identify the given values

• $Q = 1000\text{ J}$
• $m = 0.025\text{ kg}$
• $\Delta\theta = 15^\circ\text{C}$ (Note: A change of $15^\circ\text{C}$ is equivalent to a change of $15\text{ K}$)

Step 2: Substitute the values into the rearranged formula

Step 3: Perform the calculation

• First, calculate the denominator: $0.025 \times 15 = 0.375$
• Now, divide the heat energy by the result: $c = \frac{1000}{0.375}$
• $c = 2666.666...$

Rounding to one decimal place, we get $2666.7\text{ Jkg}^{-1}\text{K}^{-1}$.

Conclusion

Comparing our result with the given options, it matches option D.

Exam Tip

When dealing with specific heat capacity questions, always ensure your mass is in kilograms (kg). If the question gives you the mass in grams (g), you must divide by 1000 before plugging it into the formula. Also, remember that a change in temperature ($\Delta\theta$) in Celsius is numerically identical to a change in Kelvin, so you don't need to add 273 to the temperature change!