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Difficulty: MediumHeat Capacity and Specific Heat Capacity

A block of mass 0.5 kg0.5\text{ kg} absorbs 4500 J4500\text{ J} of heat energy as its temperature rises from 25∘C25^\circ\text{C} to 45∘C45^\circ\text{C}. What is the heat capacity of the block?

  1. A
    450 J K−1450\text{ J K}^{-1}
  2. 225 J K−1225\text{ J K}^{-1}Answer
  3. C
    112.5 J K−1112.5\text{ J K}^{-1}
  4. D
    225 J kg−1 K−1225\text{ J kg}^{-1}\text{ K}^{-1}

Answer

225 J K−1225\text{ J K}^{-1}
Heat capacity (CC) is defined as thermal energy absorbed divided by temperature change: C=QΔT=4500 J45 K−25 K=225 J K−1C = \frac{Q}{\Delta T} = \frac{4500\text{ J}}{45\text{ K} - 25\text{ K}} = 225\text{ J K}^{-1}.

Step-by-Step Solution

1
Calculate the temperature change (ΔT\Delta T).
ΔT=45∘C−25∘C=20∘C=20 K\Delta T = 45^\circ\text{C} - 25^\circ\text{C} = 20^\circ\text{C} = 20\text{ K}
Heat capacity depends on the temperature change in Kelvin or degrees Celsius.
2
Apply the heat capacity formula C=QΔTC = \frac{Q}{\Delta T}.
C=4500 J20 K=225 J K−1C = \frac{4500\text{ J}}{20\text{ K}} = 225\text{ J K}^{-1}
Heat capacity (CC) measures the heat required to raise the temperature of the entire body by 1 K1\text{ K}, regardless of mass.

Key Concept

Heat capacity (CC) represents the energy required to change an entire object's temperature by one kelvin (C=QΔTC = \frac{Q}{\Delta T}), whereas specific heat capacity (cc) is per unit mass (c=QmΔTc = \frac{Q}{m\Delta T}).
Estimated Time:1m 0s
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Topics

Heat Capacity and Specific Heat Capacity

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