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Draw a graph of variation of specific heat capacity of water with temperature and define calorie.
Solution
The old unit of heat was calorie and one calorie was earlier defined to be "the amount of heat required to raise the temperature of $1 \mathrm{~g}$ of water by $1^{\circ} \mathrm{C} .^{\prime}$
Variation of specific heat capacitor of water with temperature
The specific heat of water varies slightly with temperature hence, for a precise definition of calorie it was therefore necessary to specify the unit temperature interval.
Precise definition of Calorie : "The amount of heat required to raise the temperature of $1 \;gram$ of water from $14.5^{\circ} \mathrm{C}$ to $15.5^{\circ} \mathrm{C}$."
Unit of calorie is $\mathrm{J}$.
The specific heat capacity of water is $4186 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$ means $4.186 \mathrm{~J} \mathrm{~g}^{-1} \mathrm{~K}^{-1}$
From $\mathrm{W}=\mathrm{JH}$, the amount of work needed to produce $1 $$cal $of heat is called mechanical equiva lent of heat.
$\therefore \mathrm{W}=\mathrm{J}[\because \mathrm{H}=1$ calorie $]$
Hence, there are two units of heat, Joule and Calorie and for its change $1$ calories $=4.186 \mathrm{~J}$ heat is needed.
