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Difficulty: MediumHeat Capacity and Specific Heat Capacity

A solid metal component of mass 0.6 kg0.6\text{ kg} absorbs 5400 J5400\text{ J} of thermal energy when its temperature increases from 30∘C30^\circ\text{C} to 75∘C75^\circ\text{C}. Calculate the heat capacity of the component in J K−1\text{J K}^{-1}.

Answer: 120 J/K

Answer

The heat capacity of the metal component is 120 J K−1120\text{ J K}^{-1}.
Heat capacity (CC) is calculated by dividing the total thermal energy absorbed (Q=5400 JQ = 5400\text{ J}) by the resulting temperature change (ΔT=75∘C−30∘C=45 K\Delta T = 75^\circ\text{C} - 30^\circ\text{C} = 45\text{ K}). Performing the division yields C=540045=120 J K−1C = \frac{5400}{45} = 120\text{ J K}^{-1}. Note that the mass (0.6 kg0.6\text{ kg}) is not included in the denominator because heat capacity refers to the entire object, unlike specific heat capacity.

Step-by-Step Solution

1
Determine the change in temperature
ΔT=75∘C−30∘C=45 K\Delta T = 75^\circ\text{C} - 30^\circ\text{C} = 45\text{ K}
Heat capacity depends on the temperature difference through which heat energy is absorbed.
2
Apply the definition of heat capacity
C=QΔTC = \frac{Q}{\Delta T}
Heat capacity (CC) is defined as the thermal energy required to raise the temperature of the entire body by 1 K1\text{ K} (or 1∘C1^\circ\text{C}).
3
Substitute the given thermal energy and temperature change
C=5400 J45 K=120 J K−1C = \frac{5400\text{ J}}{45\text{ K}} = 120\text{ J K}^{-1}
Dividing total energy by total temperature rise gives heat capacity.

Key Concept

Heat capacity (CC) represents the thermal energy needed to change a body's temperature by one unit (C=Q/ΔTC = Q / \Delta T), whereas specific heat capacity (cc) is heat capacity per unit mass (c=C/mc = C / m).
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Topics

Heat Capacity and Specific Heat Capacity

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