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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: 9780137488179당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Giancoli Douglas 5th editionCh. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law문제 7b
17장, 문제 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?

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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 = T0 + L - L0L100 - L0 ∗ 100, where T is the temperature, L0 is the length of the column at 0°C, L100 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, L0 = 12.61 cm, L100 = 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 - L0 = 14.40 - 12.61 cm.
Calculate the difference between the length at 100°C and the length at 0°C: L100 - L0 = 22.79 - 12.61 cm.
Substitute the results from the previous steps into the formula to find the temperature: T = 0 + 14.40 - 12.6122.79 - 12.61 ∗ 100. Simplify the expression to determine the temperature.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.
추천 영상:
가이드 코스
05:21
Volume Thermal Expansion

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.
추천 영상:
가이드 코스
07:31
Linear Thermal Expansion

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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가이드 코스
03:47
Expanding Steel Measuring Tape
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