At 0^ ^ ^ C , the density of water is 0.998 g cm^ -3 , while at 4^ ^ ^ C it is 1.000 g cm^ -3 . Determine the average coefficient of volume expansion of water over the temperature range of 0 to 4^ ^ ^ C .

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Quantrex Academy · Accepted Answer

Correct answer: D. -5 × 10^ -4 ^ ^ ^ ^ -1

The relation between volume and temperature is given by:

V_2 = V_1(1 + \gamma \Delta T)

Since mass

m

remains constant, volume is inversely proportional to density (

V = \dfrac{m}{\rho}

). Substituting this into the equation, we get:

\dfrac{m}{\rho_2} = \dfrac{m}{\rho_1}(1 + \gamma \Delta T)

\dfrac{\rho_1}{\rho_2} = 1 + \gamma \Delta T

Substituting the given values

\rho_1 = 0.998 \text{ g cm}^{-3}

at

0^{}^{{}^{\circ}}\text{C}

,

\rho_2 = 1.000 \text{ g cm}^{-3}

at

4^{}^{{}^{\circ}}\text{C}

, and

\Delta T = 4^{}^{{}^{\circ}}\text{C}

:

\dfrac{0.998}{1.000} = 1 + \gamma (4)

0.998 = 1 + 4\gamma

4\gamma = 0.998 - 1

4\gamma = -0.002

\gamma = -0.0005 ^{}^{{}^{\circ}}\textC^{-1} = -5 \times 10^{-4} ^{}^{{}^{\circ}}\textC^{-1}

At 0^ ^ ^ C , the density of water is 0.998 g cm^ -3 , while at 4^...

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