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Standard XII

Physics

Area and Volume Expansion

The density o...

Question

The density of water at $0^{\circ} C$ is 0.998 g $c m^{- 3}$ and at $4^{\circ} C$ is 1.000 g $c m^{- 3}$ . Calculate the average coefficient of volume expansion of water in the temperature range 0 to $4^{C}$ .

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Solution

$f_{0}^{\circ} C = 0.998 g / c m^{3}$

$f_{4}^{\circ} C = 1 g / c m^{3}$

We know, $f_{0}^{\circ} = \frac{f_{4}^{\circ}}{1 + γ Δ t}$

$\Rightarrow 0.998 = \frac{1}{1 + γ . 4}$

$\Rightarrow 1 + 4 γ = \frac{1}{0.998}$

$\Rightarrow 4 γ = (\frac{1}{0.998}) - 1$

$\Rightarrow γ = 0.0005 = 5 \times 10^{- 4}$

As density decreases

$γ = - 5 \times 10^{- 4}$

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The density of water at 0∘ C is 0.998 g cm−3 and at 4∘ C is 1.000 g cm−3. Calculate the average coefficient of volume expansion of water in the temperature range 0 to 4C.

f0 ∘C=0.998 g/cm3 f4 ∘C=1g/cm3 We know, f0 ∘=f4 ∘1+γΔt ⇒ 0.998=11+γ.4 ⇒ 1+4γ=10.998 ⇒ 4γ=(10.998)−1 ⇒ γ=0.0005=5×10−4 As density decreases γ=−5×10−4

The density of water at $0^{\circ} C$ is 0.998 g $c m^{- 3}$ and at $4^{\circ} C$ is 1.000 g $c m^{- 3}$ . Calculate the average coefficient of volume expansion of water in the temperature range 0 to $4^{C}$ .