Chapter 13, Problem 74GP

To determine

To Find: The percentage error.

Answer to Problem 74GP

The percentage error in a measurement of volume is $1.26\text{ \%}$ .

Explanation of Solution

Given information:

Temperature $T_1={20}^{\circ }\text{C}$ .

Temperature $T_2\text{ =}{80}^{\circ }\text{C}$ .

Quantity of water, $V_0=300\text{ mL}$ .

Expansion coefficient, $\beta =210\times {10}^{-6}{\text{ °C}}^{\text{-1}}$ .

Formula used:

  $\%\text{ error }=\frac{\Delta V}{V_0}\times 100$

Here, $V_0$ is the quantity of water.

  $\Delta V$ is the change in the volume.

Calculation:

Fuel a cup with water at ${20}^{\text{o}}\text{C}$ , is 300 ml of cool water. Now the cup is heated to ${80}^{\circ }C$ and due to that heating, cup and water both are heated due to thermal expansion. Some of the water will overflow from the cup due to the heating. Volume of water that will overflow from the cup is called $\text{ΔV}$

  $\begin{array}{l}\Delta V=V_0\times \beta \times \Delta T\\ \Delta V=300\times {10}^{-3}\times 210\times {10}^{-6}\times (80-20)\\ \Delta V=0.00378\text{ L}\end{array}$

This is the error in the volume which is determined by using hot water.

  $\%\text{ error }=\frac{0.00378}{0.3}\times 100=1.26\text{ \%}$

Conclusion:

Thus, the percentage error in a measurement of volume is $1.26\text{ \%}$ .