# JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Thermal Capacity and Water Equivalent

Thermal Capacity and Water Equivalent

Category : JEE Main & Advanced

(1) Thermal capacity : It is defined as the amount of heat required to raise the temperature of the whole body (mass m) through ${{0}^{o}}C$ or 1K.

Thermal capacity $=mc=\mu C=\frac{Q}{\Delta \theta }$

The value of thermal capacity of a body depends upon the nature of the body and its mass.

Dimension : $[M{{L}^{2}}{{T}^{-2}}{{\theta }^{-1}}]$, Unit : cal/$^{o}C$ (practical)  Joule/k (S.I.)

(2) Water Equivalent : Water equivalent of a body is defined as the mass of water which would absorb or evolve the same amount of heat as is done by the body in rising or falling through the same range of temperature. It is represented by W.

If m = Mass of the body, c = Specific heat of body, $\Delta \theta =$ Rise in temperature.

Then heat given to body $\Delta Q=mc\Delta \theta$                 ... (i)

If same amount of heat is given to W gm of water and its temperature also rises by  $\Delta \theta$.

Then heat given to water $Q=W\times 1\times \Delta \theta$ ...(ii)     [As ${{c}_{\text{water}}}=1$]

From equation (i) and (ii)  $\Delta Q=mc\Delta \theta =W\times 1\times \Delta \theta$

$\Rightarrow$ Water equivalent (W) = mc gm

(i) Unit : Kg (S.I.)               Dimension : $[M{{L}^{0}}{{T}^{0}}]$

(ii) Unit of thermal capacity is J/kg while unit of water equivalent is kg.

(iii) Thermal capacity of the body and its water equivalent are numerically equal.

(iv) If thermal capacity of a body is expressed in terms of mass of water it is called water-equivalent of the body.

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