contestada

Two litres of water, initially at 20 °C, is heated to 40 °C. Determine thevolume of water at 40 °C if the coefficient of volumetric expansion ofwater within this range is 30 x 10-9 °C.

Respuesta :

Given data

*The given initial volume of water is V_1 = 2 L

*The given initial temperature of the water is T_i = 20 °C

*The given final temperature of the water is T_f = 40 °C

*The coefficient of volumetric expansion of water is

[tex]\alpha=30\times10^{-9}^{}\text{C}[/tex]

The formula for the volumetric expansion is given as

[tex]\frac{\Delta V}{V}=\alpha(T_f-T_i)[/tex]

Substitute the known values in the above expression as

[tex]\begin{gathered} \frac{\Delta V}{V_1}=30\times10^{-9}\times(40^0-20^0) \\ V_2-V_1=6\times10^{-7}V_1 \\ V_2=6\times10^{-7}V_1+V_1^{} \\ =V_1(6\times10^{-7}+1) \\ =2.00\text{ L} \end{gathered}[/tex]