Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law

Problem 7b

Chapter 17, Problem 7b

In an alcohol-in-glass thermometer, the alcohol column has length 12.61 cm at 0.0°C and length 22.79 cm at 100.0°C. What is the temperature if the column has length 14.40 cm?

Verified step by step guidance

Determine the relationship between the length of the alcohol column and the temperature. The length of the column is linearly proportional to the temperature, so we can use the formula:

T = T 0 + \frac{L - L_{0}}{L_{100} - L_{0}} * 100

, where

T

is the temperature,

L_{0}

is the length of the column at 0°C,

L_{100}

is the length of the column at 100°C, and

L

is the length of the column at the unknown temperature.

Substitute the given values into the formula. From the problem,

L_{0} = 12.61

cm,

L_{100} = 22.79

cm, and

L = 14.40

cm.

Calculate the difference between the length at the unknown temperature and the length at 0°C:

L - L_{0} = 14.40 - 12.61

cm.

Calculate the difference between the length at 100°C and the length at 0°C:

L_{100} - L_{0} = 22.79 - 12.61

cm.

Substitute the results from the previous steps into the formula to find the temperature:

T = 0 + \frac{14.40 - 12.61}{22.79 - 12.61} * 100

. Simplify the expression to determine the temperature.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Thermal Expansion

Thermal expansion refers to the increase in volume or length of a substance as its temperature rises. In the context of a thermometer, the liquid (alcohol) expands uniformly with temperature changes, allowing for accurate measurement of temperature based on the length of the liquid column.

Linear Interpolation

Linear interpolation is a mathematical method used to estimate unknown values that fall within two known values. In this case, it can be applied to determine the temperature corresponding to a specific length of the alcohol column by using the known lengths at 0.0°C and 100.0°C.

Calibration of Thermometers

Calibration of thermometers involves setting a scale based on known reference points, such as the freezing and boiling points of water. For the alcohol-in-glass thermometer, the lengths of the alcohol column at these reference temperatures are used to create a linear scale for measuring other temperatures.

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