A steel tape is calibrated at 20^∘ C. On a cold day when the...

A steel tape is calibrated at $20^{\circ} \mathrm{C}$. On a cold day when the temperature is $-15^{\circ} \mathrm{C}$, what will be the percent error in the tape? $\alpha_{\text {steel }}=1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$. For a temperature change from $20^{\circ} \mathrm{C}$ to $-15^{\circ} \mathrm{C}$, we have $\Delta T=-35^{\circ} \mathrm{C}$. Then, $$ \frac{\Delta L}{L_{0}}=\alpha \Delta T=\left(1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}\right)\left(-35^{\circ} \mathrm{C}\right)=-3.9 \times 10^{-4}=-0.039 \% $$

A steel tape is calibrated at $20^{\circ} \mathrm{C}$. On a cold day when the temperature is $-15^{\circ} \mathrm{C}$, what will be the percent error in the tape? $\alpha_{\text {steel }}=1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}$.
For a temperature change from $20^{\circ} \mathrm{C}$ to $-15^{\circ} \mathrm{C}$, we have $\Delta T=-35^{\circ} \mathrm{C}$. Then,
$$
\frac{\Delta L}{L_{0}}=\alpha \Delta T=\left(1.1 \times 10^{-5}{ }^{\circ} \mathrm{C}^{-1}\right)\left(-35^{\circ} \mathrm{C}\right)=-3.9 \times 10^{-4}=-0.039 \%
$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Percent Error Calculation

Percent error calculation is a measure used to express the relative change in a quantity as a percentage of the original value. In the context of thermal expansion, it helps quantify how much the dimensions of a calibrated instrument, such as a steel tape, deviate from its calibrated length due to temperature changes.

Thermal Expansion

Thermal expansion is the phenomenon where a material changes its dimensions (length, area, volume) in response to a change in temperature. This concept is crucial in understanding how materials behave under thermal stress, which affects their performance and the accuracy of measurements in various applications.

Coefficient of Linear Expansion

The coefficient of linear expansion is a material constant that quantifies the change in length per unit length per degree change in temperature. It is used in the formula ?L = ?L??T to determine how much a material contracts or expands with temperature variations.

Temperature Change

Temperature change refers to the difference between the initial and final temperatures that a material experiences. This change is a key factor in calculating thermal expansion, as it directly influences the extent to which a material expands or contracts.

Transcript

Please give Ace some feedback