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Difficulty: EasyHeat Capacity and Specific Heat Capacity

A metal block of mass 4.0 kg4.0\text{ kg} absorbs 12 kJ12\text{ kJ} of thermal energy, causing its temperature to rise by 15 K15\text{ K}. What is the specific heat capacity of the metal block in J kg−1K−1\text{J kg}^{-1}\text{K}^{-1}?

Answer: 200 J kg^-1 K^-1

Answer

The specific heat capacity of the metal block is 200 J kg−1K−1200\text{ J kg}^{-1}\text{K}^{-1}.
Specific heat capacity cc is determined using c=QmΔTc = \frac{Q}{m \Delta T}. Substituting Q=12,000 JQ = 12,000\text{ J}, m=4.0 kgm = 4.0\text{ kg}, and ΔT=15 K\Delta T = 15\text{ K} yields c=120004.0×15=200 J kg−1K−1c = \frac{12000}{4.0 \times 15} = 200\text{ J kg}^{-1}\text{K}^{-1}.

Step-by-Step Solution

1
Convert given energy to standard SI units
Q=12 kJ=12,000 JQ = 12\text{ kJ} = 12,000\text{ J}
Calculation of specific heat capacity requires heat energy in Joules.
2
Relate heat energy, mass, specific heat capacity, and temperature change
Q=mcΔT  ⟹  c=QmΔTQ = m c \Delta T \implies c = \frac{Q}{m \Delta T}
Specific heat capacity cc represents heat energy per unit mass per Kelvin temperature change.
3
Substitute the values and compute the result
c=120004.0×15=200 J kg−1K−1c = \frac{12000}{4.0 \times 15} = 200\text{ J kg}^{-1}\text{K}^{-1}
Evaluating the expression gives 200 J kg−1K−1200\text{ J kg}^{-1}\text{K}^{-1}.

Key Concept

Specific heat capacity is the quantity of heat required to raise the temperature of 1 kg1\text{ kg} of a substance by 1 K1\text{ K}, expressed as c=QmΔTc = \frac{Q}{m \Delta T}.
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Topics

Heat Capacity and Specific Heat Capacity

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