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

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