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Difficulty: MediumHeat Capacity and Specific Heat Capacity

A solid metal block absorbs 3600 J3600\text{ J} of thermal energy when its temperature increases from 20∘C20^\circ\text{C} to 60∘C60^\circ\text{C}. If the block has a mass of 2.0 kg2.0\text{ kg}, what is the heat capacity of the block?

  1. 90 J K−190\text{ J K}^{-1}Answer
  2. B
    45 J K−145\text{ J K}^{-1}
  3. C
    180 J K−1180\text{ J K}^{-1}
  4. D
    60 J K−160\text{ J K}^{-1}

Answer

The heat capacity of the block is 90 J K−190\text{ J K}^{-1}.
The correct answer is 90 J K−190\text{ J K}^{-1} because heat capacity is defined as C=QΔTC = \frac{Q}{\Delta T}. Dividing the absorbed heat of 3600 J3600\text{ J} by the temperature change of 40 K40\text{ K} yields 90 J K−190\text{ J K}^{-1}.

Step-by-Step Solution

1
Calculate the temperature change (ΔT\Delta T)
ΔT=60∘C−20∘C=40 K\Delta T = 60^\circ\text{C} - 20^\circ\text{C} = 40\text{ K}
Heat capacity depends on the change in temperature, not the initial or final temperature values.
2
Apply the formula for total heat capacity (C=QΔTC = \frac{Q}{\Delta T})
C=3600 J40 K=90 J K−1C = \frac{3600\text{ J}}{40\text{ K}} = 90\text{ J K}^{-1}
Heat capacity CC measures the total thermal energy required to raise the entire body's temperature by one degree Kelvin (or Celsius).

Key Concept

Heat capacity (CC) represents the heat quantity needed to change a body's temperature by 1 K1\text{ K} (C=QΔTC = \frac{Q}{\Delta T}), whereas specific heat capacity (cc) is heat capacity per unit mass (c=QmΔTc = \frac{Q}{m\Delta T}).
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Topics

Heat Capacity and Specific Heat Capacity

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