Q. 17

# The density of water at 0°C is 0.998 g cm^{–3} and at 4°C is 1.000g cm^{–3}. Calculate the average coefficient of volume expansion of water in the temperature range 0 to 4°C.

Answer :

**Given:**

Density of water at 0 °C: ρ_{0} = 0.998 g cm^{-3}

Density of water at 4 °C: ρ_{4} = 1.000 g cm^{-3}

Temperature Range: θ = 4 °C

**Formula used:**

We know that the formula for volume expansion is:

Where V_{θ} is the volume at θ °C

V_{0} is the volume at 0 °C

γ is the coefficient of volume expansion

Now, since

On substituting :

As density decreases γ = -5 x 10^{-4} ° C^{-1}

**Hence the average** **Calculate the average coefficient of volume expansion of water in the temperature range 0 to 4°C is**

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Show that moment of inertia of a solid body of any shape changes with temperature as I = I_{1}(1 + 2αθ), where I, is the moment of inertia at 0°C and α is the coefficient of linear expansion of the solid.

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