Question

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.

Answer 1

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

`\alpha=30*10^(-9)^{}\text{C}`

The formula for the volumetric expansion is given as

`(\Delta V)/(V)=\alpha(T_f-T_i)`

Substitute the known values in the above expression as

`\begin{gathered} (\Delta V)/(V_1)=30*10^(-9)*(40^0-20^0) \\ V_2-V_1=6*10^(-7)V_1 \\ V_2=6*10^(-7)V_1+V_1^{} \\ =V_1(6*10^(-7)+1) \\ =2.00\text{ L} \end{gathered}`