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

Specific Heat of Solids

Category : JEE Main & Advanced

When a solid is heated through a small range of temperature, its volume remains more or less constant. Therefore specific heat of a solid may be called its specific heat at constant volume \[{{C}_{V}}\].

(1) From the graph it is clear that at \[T=0,\,\,{{C}_{V}}\] tends to zero

(2) With rise in temperature, \[{{C}_{V}}\] increases and at a particular temperature (called Debey's temperature) it becomes constant = 3R = 6 cal/mole \[\times \] kelvin = 25 J/mole \[\times \] kelvin

(3) For most of the solids, Debye temperature is close to room temperature.

(4) Dulong and Petit law : Average molar specific heat of all metals at room temperature is constant, being nearly equal to 3R = 6 cal. \[mol{{e}^{-1}}\,{{K}^{-1}}\] = 25 J \[mol{{e}^{-1}}\,{{K}^{-1}}\], where R is gas constant for one mole of the gas. This statement is known as Dulong and Petit law.

(5) Debey's law : It was observed that at very low temperature molar specific heat \[\propto {{T}^{3}}\] exception are Sn, Pb and Pt)

(6) Specific heat of ice : In C.G.S. \[{{c}_{\text{ice}}}=0.5\,\frac{cal}{gm\times {}^\circ C}\]

In S.I. \[{{c}_{ice}}==500\,\frac{cal}{kg\times {}^\circ C}=2100\,\frac{Joule}{kg\times {}^\circ C}\].  

Specific heat of some solids at room temperature and atmospheric pressure

Substance Specific heat \[\mathbf{(J-k}{{\mathbf{g}}^{\mathbf{-1}}}\,{{\mathbf{K}}^{\mathbf{-1}}}\mathbf{)}\] Molar specific heat \[\mathbf{(J-g}\,\,\mathbf{mol}{{\mathbf{e}}^{\mathbf{-1}}}\,{{\mathbf{K}}^{\mathbf{-1}}}\mathbf{)}\]
Aluminium 900.0 24.4
Copper 386.4 24.5
Silver 236.1 25.5
Lead 127.7 26.5
Tungsten 134.4 24.9


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