A column of liquid is found to expand linearly on heating 5.25 cm for a 10.0^∘ F rise in tempera

step 1 Since there is expansion of height in column of liquid, so we will first calculate the increase

A column of liquid is found to expand linearly on heating...

A column of liquid is found to expand linearly on heating $5.25$ $\mathrm{cm}$ for a $10.0^{\circ} \mathrm{F}$ rise in temperature. If the initial temperature of the liquid is $98.6^{\circ} \mathrm{F}$, what will the final temperature be in ${ }^{\circ} \mathrm{C}$ if the liquid has expanded by $18.5 \mathrm{~cm}$ ?

Key Concepts

Proportional Relationships

Proportional relationships describe scenarios where one quantity changes directly with another. In the context of thermal expansion, if the expansion is linear, the change in length is directly proportional to the change in temperature. This relationship allows for determining unknown temperature changes when the corresponding change in length is given.

Temperature Scale Conversion

Temperature scale conversion is the process of converting temperature measurements from one scale to another, such as from Fahrenheit to Celsius. This conversion is important because different systems and scientific contexts may require temperatures to be expressed in a particular scale, and correct conversions ensure accurate communication and interpretation of data.

Thermal Expansion

Thermal expansion is the tendency of matter to change its dimensions in response to a change in temperature. When a substance, such as a liquid, is heated, its particles move more vigorously, leading to an increase in volume or length. This concept is fundamental in physics and engineering, influencing applications from material design to everyday temperature measurements.

Coefficient of Linear Thermal Expansion

The coefficient of linear thermal expansion quantifies how much a material’s length changes per unit length for each degree of temperature change. It is a constant for a given material under specific conditions and allows for calculation of dimensional changes due to temperature variations using the linear expansion formula.

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