Question

Two mercury-expansion thermometers have identical reservoirs and cylindrical tubes made of the same glass but of different diameters. Which of the two thermometers can be graduated to a better resolution? a) The thermometer with the smaller diameter tube will have better resolution. b) The thermometer with the larger diameter tube will have better resolution. c) The diameter of the tube is irrelevant; it is only the volume expansion coefficient of mercury that matters. d) Not enough information is given to tell.

Short answer

Answer: a) The thermometer with the smaller diameter tube will have better resolution.

Step-by-step solution

Understanding the concept of resolution

Resolution refers to the smallest change in temperature that can be detected by a thermometer. In a mercury-expansion thermometer, this is determined by the length of the mercury column in the capillary tube. The length of the mercury column is affected by the diameter of the tube.

Analyzing the relationship between diameter and resolution

In a mercury-expansion thermometer, the mercury expands when heated. This expansion causes the mercury column in the tube to rise. If the diameter of the tube is smaller, a smaller amount of volume change in the mercury would result in a significant increase in the length of the column. This means the thermometer with the smaller diameter tube would be able to detect smaller changes in temperature, hence having a better resolution.

Choosing the correct answer

Based on the analysis in Step 2, we can conclude that the thermometer with the smaller diameter tube will have a better resolution. Therefore, the correct answer is: a) The thermometer with the smaller diameter tube will have better resolution.

Key concepts

Mercury-expansion thermometer

In the realm of temperature measurement, a mercury-expansion thermometer plays a vital role. This type of thermometer uses mercury, a liquid metal, due to its reliable thermal properties.
As temperature rises, the mercury in the thermometer expands, moving up through the narrow tube.
This movement translates the thermal energy, or temperature, of the substance being measured into a visible length of liquid mercury in the tube.

• Mercury's use is favored because of its uniform expansion over a wide temperature range.
• It remains in liquid form across a broad spectrum of temperatures.
• Because it doesn’t wet the thermometer’s glass, it allows clear and consistent readings.

These properties make mercury-expansion thermometers precise tools for scientific and other detailed temperature measurement tasks.

Volume expansion coefficient

The volume expansion coefficient is a crucial aspect of liquid-based thermometers like the mercury-expansion type. It describes how much the volume of a liquid changes as the temperature changes.
In essence, it measures the responsiveness of the liquid to temperature changes, telling us how sensitive the liquid column in the thermometer will be.

• In the case of mercury, the volume expansion coefficient is consistent over its operating temperature range.
• This predictability contributes to its effectiveness in thermometric applications.
• A higher volume expansion coefficient would mean the liquid expands more with temperature and provides a more pronounced change in the column length.

Understanding this concept helps in appreciating the precision thermometers achieve in temperature readings.

Temperature measurement

Temperature measurement is a fundamental scientific activity utilized in many fields, from weather forecasting to manufacturing. Using a thermometer for temperature measurement involves checking how much the mercury rises within the tube, thus indicating the temperature.
Key features of effective temperature measurement include:

• Accuracy: The thermometer must reflect the true temperature without systematic errors.
• Resolution: The ability to detect small changes in temperature, crucial in sensitive applications.
• Range: A thermometer should cover the temperature spectrum of its intended use.

When utilizing a mercury-expansion thermometer, its design critically influences these aspects, ensuring precise and reliable readings. The instruments are thus tailor-made for specific tasks, where minute changes in temperature need to be precisely detected.

Cylindrical tube diameter

The cylindrical tube diameter in a mercury-expansion thermometer plays a significant role in determining the resolution of the device. Simply put, resolution refers to the smallest temperature change detectable by the thermometer.
Here's why the tube's diameter is so important:

• Smaller diameter tubes allow for higher resolution because a small change in the volume of mercury results in a larger movement of the mercury column.
• This increased movement equates to a higher sensitivity in temperature detection.
• Larger diameters require more mercury volume change for the same column rise, decreasing resolution.

By opting for a thermometer with a smaller cylindrical tube diameter, one can achieve better sensitivity and finer measurements, critical in fields demanding such precision.