NEET-XII-Physics
23: Heat and Temperature
- #17The density of water at 0°C is 0.998 g cm-3 and at 4°C is 1.000 g cm-1. Calculate the average coefficient of volume expansion of water in the temperature range of 0 to 4°C.Ans : Given:
Density of water at 0°C, ( f0)= 0.998 g cm-3
Density of water at 4°C, (f4) = 1.000 g cm-3
Change in temperature, (Δt) = 4oC
Let the average coefficient of volume expansion of water in the temperature range of 0 to 4°C be γ.
`` \,\mathrm{\,We\,}\,\mathrm{\,know\,}:{f}_{4}={f}_{0}\left(1+\gamma ∆t\right)``
`` \Rightarrow {f}_{0}=\frac{{f}_{4}}{1+\gamma ∆t}``
`` \Rightarrow 0.998=\frac{1}{1+\gamma .4}``
`` \Rightarrow 1+4\gamma =\frac{1}{0.998}``
`` \Rightarrow 4\gamma =\left(\frac{1}{0.998}\right)-1``
`` \Rightarrow \gamma =0.0005=5\times {10}^{-4}{}^{\,\mathrm{\,o\,}}{\,\mathrm{\,C\,}}^{-1}``
As the density decreases,
`` \gamma =-5\times {10}^{-4}{}^{\,\mathrm{\,o\,}}{\,\mathrm{\,C\,}}^{-1}``
Therefore,the average coefficient of volume expansion of water in the temperature range of 0 to 4°C will be `` \gamma =-5\times {10}^{-4}``oC-1.
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