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Difficulty: MediumHeat Capacity and Specific Heat Capacity

When equal masses of two different substances absorb equal quantities of heat energy without undergoing a phase change, the substance with the lower specific heat capacity will experience a larger temperature rise.

Answer: Answer

Answer

The statement is true because temperature change is inversely proportional to specific heat capacity when equal heat energy is supplied to equal masses.
According to the heat equation Q=mcΔTQ = m c \Delta T, the temperature change is given by ΔT=Qmc\Delta T = \frac{Q}{m c}. For identical values of mass mm and heat input QQ, temperature change ΔT\Delta T is inversely proportional to specific heat capacity cc. Therefore, a substance with a lower specific heat capacity will undergo a larger temperature rise.

Step-by-Step Solution

1
Identify the formula relating heat energy absorbed to mass, specific heat capacity, and temperature change.
The relationship is Q=mcΔTQ = m c \Delta T.
This fundamental equation models sensible heat exchange in matter.
2
Isolate the temperature change variable ΔT\Delta T.
ΔT=Qmc.\Delta T = \frac{Q}{m c}.
Expressing ΔT\Delta T explicitly allows direct analysis of how specific heat capacity influences temperature rise.
3
Determine the functional dependence of ΔT\Delta T on cc under constant mm and QQ.
ΔT∝1c.\Delta T \propto \frac{1}{c}.
Since ΔT\Delta T and cc are inversely proportional, a smaller specific heat capacity cc leads to a larger temperature increase ΔT\Delta T.

Key Concept

Inverse proportionality between specific heat capacity and temperature change for a given mass and heat input.
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Topics

Heat Capacity and Specific Heat Capacity

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