# JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Specific Heat

Specific Heat

Category : JEE Main & Advanced

When a body is heated it's temperature rises (except during a change in phase).

(1) Gram specific heat : The amount of heat energy  required to raise the temperature of unit mass of a body through ${{1}^{o}}C$ (or K) is called specific heat of the material of the body.

If Q heat changes the temperature of mass m by $\Delta \theta$ then specific heat $c=\frac{Q}{m\Delta \theta }$

(i) Units : Calorie/gm $\times {{\,}^{o}}C$ (practical), J/kg $\times$ K (S.I.)

Dimension : $[{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}]$

(ii) For an infinitesimal temperature change $d\theta$ and corresponding quantity of heat dQ.

Specific heat $c=\frac{1}{m}.\frac{dQ}{d\theta }$

(2) Molar specific heat : Molar specific heat of a substance is defined as the amount of heat required to raise the temperature of one gram mole of the substance through a unit degree it is represented by (capital) C.

Molar specific heat (C) $=M\times \text{Gram specific heat}$(c)

(M = Molecular mass of substance)

$C=M\frac{Q}{m\Delta \theta }=\frac{1}{\mu }\frac{Q}{\Delta \theta }$    $\left( \text{where,}\,\text{Number of moles }\mu =\frac{m}{M} \right)$

Units : calorie/mole $\times {{\,}^{o}}C$ (practical); J/mole $\times$ kelvin (S.I.)

Dimension : $[M{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}]$

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