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Heat Capacity, Specific Heat Capacity

Heat capacity

Heat capacity is the amount of heat to be supplied for an object to change a specific amount of temperature:

C=limΔT0ΔQΔTC=\lim\limits_{\Delta T\to 0}\frac{\Delta Q}{\Delta T}

where QQ is thermal energy, and TT is temperature. Its SI unit is joule per kelvin (J/KJ/K).

The change in thermal energy equals to heat capacity times the change in temperature:

Q=CΔTQ=C\Delta T

A specific material with different masses have different heat capacities. Boiling a full kettle of water takes more time (requires more heat) than boiling half kettle of water. Different materials also have different heat capacities. It is easier to increase the temperature of steel than water, if they have the same amount of mass.

Specific heat capacity

Specific heat capacity is heat capacity divided by the mass of the object.

c=Cmc=\frac{C}{m}

Its SI unit is joule per kelvin J/(kgK)J/(kg\cdot K).

Therefore, the change in thermal energy equals to mass times specific heat capacity times the change in temperature:

Q=mcΔTQ=mc\Delta T

Here is a table of specific heat capacity for common materials:

Materialwater at 25 C25\ ^\circ Cbrasssteel
Specific heat capacity J/(kgKJ/(kg\cdot K)4182380466