Chapter 13, Problem 102A

To determine

To find: the water level drop or risen.

Answer to Problem 102A

The water level has risen to a level of $0.735\text{mL}$ when the bottle and water are heated to $50.0°\text{C}$ .

Explanation of Solution

Given:

Volume of water is $\text{1}00\text{ mL}$ .

Volume of soft glass beaker is $800.0\text{mL}$ .

Formula used:

The coefficient of volume expression is given by,

  $\beta =\frac{\Delta V}{V_1\Delta T}$.......(1)

Here, $\Delta V$ is changed in volume, $V_1$ is the original volume and $\Delta T$ is the change in temperature.

Calculation:

Equation (1) can be rewritten as,

  $\Delta V=\beta V_1\Delta T$.......(2)

Substitute $210\times {10}^{-6}{\text{°C}}^{\text{-1}}$ for $\beta$ , $100\text{mL}$ for $V_1$ , $35.0°\text{C}$ for $\Delta T_1$ and evaluate $\Delta V$ in equation (2)

  $\begin{array}{l}\Delta V=\left(210\times {10}^{-6}°{\text{C}}^{-1}\right)\left(100.0\text{mL}\right)\left(35.0°\text{C}\right)\\ \Delta V=0.735\text{mL}\end{array}$

Conclusion:

Hence, the water level has risen to a level of $0.735\text{mL}$ when the bottle and water are heated to $50.0°\text{C}$ .