Question

A metal piece of thermal capacity 40 JK\(^{-1}\), absorbs 800 J of heat. Calculate the rise in the temperature of this metal piece.

Hint:

Distinguish between specific heat capacity (per unit mass, \(c\)) and thermal capacity (for the whole object, \(C'\)). The formulas are \(Q=mc\Delta T\) and \(Q=C'\Delta T\). Here, the problem gives thermal capacity directly, making the calculation simpler.

Answer 1

Step 1: Understanding the Concept:
Thermal capacity (or Heat capacity) is the amount of heat required to raise the temperature of the entire body by \( 1\text{ K} \).
Step 2: Key Formula or Approach:
The formula relating heat absorbed (\( Q \)), thermal capacity (\( C' \)), and change in temperature (\( \Delta T \)) is:
\[ Q = C' \cdot \Delta T \]
Step 3: Detailed Explanation:
Given values:
- Heat absorbed, \( Q = 800\text{ J} \)
- Thermal capacity, \( C' = 40\text{ JK}^{-1} \)
Rearranging the formula to find the rise in temperature (\( \Delta T \)):
\[ \Delta T = \frac{Q}{C'} \]
Substituting the values:
\[ \Delta T = \frac{800}{40} = 20\text{ K} \]
Note that a rise of \( 20\text{ K} \) is equivalent to a rise of \( 20^\circ\text{C} \).
Step 4: Final Answer:
The rise in temperature is \( 20\text{ K} \).