Heat capacity

This article deals with the heat capacity of a body. For the material property, see Specific heat capacity.

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The heat capacity Ca body is the ratio of the heat supplied to it (\Delta Q) to the temperature increase caused by it (\Delta T):

C = \frac{\mathrm dQ}{\mathrm dT}

The unit of heat capacity is J/K.

For homogeneous bodies, the heat capacity can be calculated as the product of the specific heat capacity cand the mass mthe body,

{\displaystyle C=c\cdot m,}

or as the product of its molar heat capacity {\displaystyle C_{\mathrm {m} }}and its amount of substance n:

{\displaystyle C=C_{\mathrm {m} }\cdot n}

Both specific and molar heat capacity are material constants and are tabulated in relevant reference books.

The heat capacity is an extensive state variable, so for a body composed of parts it can be calculated as the sum of the respective heat capacities C_{n}its Nparts. For the total heat capacity therefore results: {\displaystyle C_{\mathrm {ges} }}

{\displaystyle C_{\mathrm {ges} }=\sum _{n=1}^{N}C_{n}=C_{1}+C_{2}+\dotsb +C_{N}}

For layered systems such as wall constructions, the heat capacity is given per unit area, in J/(m2-K), for metre goods such as extruded heat sinks per unit length, in J/(m-K).

Determination of the heat capacity in the mixing test

The experimental determination of the heat capacity of a body shows how to deal with this quantity:

The body is first placed in boiling water ( \vartheta _{1}=100\,{\mathrm {^{\circ }C}}) until it has itself assumed this temperature. Then transfer it to a calorimeter where {\displaystyle m_{\mathrm {W} }=1\,\mathrm {kg} }Water with temperature of \vartheta_2 = 20 \, \mathrm{^\circ C}. A mixing temperature of \vartheta _{3}=30\,{\mathrm {^{\circ }C}}.

The water has therefore increased by Δ {\displaystyle \Delta T_{\mathrm {W} }=\vartheta _{3}-\vartheta _{2}=10\,\mathrm {K} }warmed.

With the known specific heat capacity of water ( {\displaystyle c_{\mathrm {W} }\approx 4{,}2\,\mathrm {\tfrac {kJ}{kg\cdot K}} }), the heat absorbed by the water is calculated as

{\displaystyle Q_{\mathrm {W} }=c_{\mathrm {W} }\cdot m_{\mathrm {W} }\cdot \Delta T_{\mathrm {W} }=42\,\mathrm {kJ} }.

This is the amount of heat the body has when it cools down by Δ {\displaystyle \Delta T_{\mathrm {K} }=\vartheta _{1}-\vartheta _{3}=70\,\mathrm {K} }released to the water, so {\displaystyle Q_{\mathrm {K} }=Q_{\mathrm {W} }=42\,\mathrm {kJ} }. Consequently, the heat capacity of the body is:

{\displaystyle C_{\mathrm {K} }={\frac {Q_{\mathrm {K} }}{\Delta T_{\mathrm {K} }}}=\mathrm {600\,{\frac {J}{K}}} }

Norm data (subject term): GND: 4188854-6 (OGND, AKS)


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