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Difficulty: HardHeat Capacity and Specific Heat Capacity

The table below presents the mass, quantity of heat absorbed, and resulting temperature change for three solid metal blocks, PP, QQ, and RR:

BlockMass (kg\text{kg})Heat Absorbed (J\text{J})Temperature Change (K\text{K})
PP0.200.208008001010
QQ0.500.50150015001515
RR0.400.40120012002020

Which of the following statements correctly compares the thermal properties of the blocks?

  1. Block PP has the highest specific heat capacity, while block QQ has the highest total heat capacity.Answer
  2. B
    Block QQ has both the highest specific heat capacity and the highest total heat capacity.
  3. C
    Block RR has the highest specific heat capacity, while block PP has the lowest total heat capacity.
  4. D
    Block PP has the lowest specific heat capacity, while block RR has the highest total heat capacity.

Answer

Block PP has the highest specific heat capacity, while block QQ has the highest total heat capacity.
The total heat capacity CC is found using C=QΔTC = \frac{Q}{\Delta T}, giving 80 J K−180\text{ J K}^{-1} for PP, 100 J K−1100\text{ J K}^{-1} for QQ, and 60 J K−160\text{ J K}^{-1} for RR. Dividing heat capacity by mass yields the specific heat capacity c=Cmc = \frac{C}{m}, resulting in 400 J kg−1 K−1400\text{ J kg}^{-1}\text{ K}^{-1} for PP, 200 J kg−1 K−1200\text{ J kg}^{-1}\text{ K}^{-1} for QQ, and 150 J kg−1 K−1150\text{ J kg}^{-1}\text{ K}^{-1} for RR. Therefore, block PP has the highest specific heat capacity and block QQ has the highest total heat capacity.

Step-by-Step Solution

1
Calculate the total heat capacity (C=QΔTC = \frac{Q}{\Delta T}) for each block
CP=80010=80 J K−1C_P = \frac{800}{10} = 80\text{ J K}^{-1}, CQ=150015=100 J K−1C_Q = \frac{1500}{15} = 100\text{ J K}^{-1}, CR=120020=60 J K−1C_R = \frac{1200}{20} = 60\text{ J K}^{-1}
Heat capacity measures the total thermal energy required to raise the entire object's temperature by 1 K1\text{ K}.
2
Calculate the specific heat capacity (c=Cm=QmΔTc = \frac{C}{m} = \frac{Q}{m \Delta T}) for each block
cP=800.20=400 J kg−1 K−1c_P = \frac{80}{0.20} = 400\text{ J kg}^{-1}\text{ K}^{-1}, cQ=1000.50=200 J kg−1 K−1c_Q = \frac{100}{0.50} = 200\text{ J kg}^{-1}\text{ K}^{-1}, cR=600.40=150 J kg−1 K−1c_R = \frac{60}{0.40} = 150\text{ J kg}^{-1}\text{ K}^{-1}
Specific heat capacity measures the heat capacity per unit mass of the material.
3
Compare the computed values
Highest specific heat capacity: Block PP (400 J kg−1 K−1400\text{ J kg}^{-1}\text{ K}^{-1}); Highest total heat capacity: Block QQ (100 J K−1100\text{ J K}^{-1}).
Block PP requires the most heat per kilogram per Kelvin, while Block QQ requires the most heat overall to raise its temperature by 1 K1\text{ K} due to its larger mass.

Key Concept

Distinction between Heat Capacity (C=QΔTC = \frac{Q}{\Delta T}) and Specific Heat Capacity (c=QmΔTc = \frac{Q}{m \Delta T})
Estimated Time:1m 30s
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Topics

Heat Capacity and Specific Heat Capacity

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