91Ó°ÊÓ

(a) Normal body temperature. The average normal body temperature measured in the mouth is \(310 \mathrm{~K}\). What would Celsius and Fahrenheit thermometers read for this temperature? (b) Elevated body temperature. During very vigorous exercise, the body's temperature can go as high as \(40^{\circ} \mathrm{C}\). What would Kelvin and Fahrenheit thermometers read for this temperature? (c) Temperature difference in the body. The surface temperature of the body is normally about \(7 \mathrm{C}^{\circ}\) lower than the internal temperature. Express this temperature difference in kelvins and in Fahrenheit degrees. (d) Blood storage. Blood stored at \(4.0^{\circ} \mathrm{C}\) lasts safely for about 3 weeks, whereas blood stored at \(-160^{\circ} \mathrm{C}\) lasts for 5 years. Express both temperatures on the Fahrenheit and Kelvin scales. (e) Heat stroke. If the body's temperature is above \(105^{\circ} \mathrm{F}\) for a prolonged period, heat stroke can result. Express this temperature on the Celsius and Kelvin scales.

Step by step solution

01

Convert Body Temperature to Celsius and Fahrenheit

Given the average body temperature is \(310 \mathrm{~K}\), in Celsius, \( C = K - 273.15 = 310 - 273.15 = 36.85 ^{\circ}C \). In Fahrenheit, use the converted Celsius value: \( F = 9/5(C) + 32 = 9/5(36.85) + 32 = 98.33 ^{\circ}F \).

02

Temperature During Vigorous Exercise

Elevated body temperature is \(40^{\circ} C\). In Kelvin, \( K = C + 273.15 = 40 + 273.15 = 313.15 K \). In Fahrenheit, \( F = 9/5(C) + 32 = 9/5(40) + 32 = 104 ^{\circ}F \).

03

Temperature Differences

Given the temperature difference is \(7^{\circ} \mathrm{C}\). This difference in Celsius is same as Kelvin, so, difference = \(7 K\). In Fahrenheit, use the difference in Celsius without adding the 32 constant: diff = \(9/5(7) = 12.6 ^{\circ}F\).

04

Blood Storage Temperatures

Temperature of blood when safely stored for 3 weeks and 5 years are \(4^{\circ} C\) and \(-160^{\circ} C\). In Fahrenheit, \( F1 = 9/5(4) + 32 = 39.2 ^{\circ}F \) and \( F2 = 9/5(-160) + 32 = -256 ^{\circ}F \). In Kelvin, \( K1 = 4 + 273.15 = 277.15 K \) and \( K2 = -160 + 273.15 = 113.15 K \).

05

Temperature Leading to Heat Stroke

Body temperature above which heat stroke can result is \(105^{\circ} F\). In Celsius, \( C = 5/9(F - 32) = 5/9(105 - 32) = 40.56^{\circ}C \). In Kelvin, \( K = C + 273.15 = 40.56 + 273.15 = 313.71 K \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Kelvin to Celsius Conversion

Understanding the relationship between Kelvin and Celsius is crucial in physics and everyday life. Kelvin is the base unit of temperature in the International System of Units (SI), and it's an absolute scale starting at absolute zero, the theoretical point where all kinetic motion in atoms ceases.

To convert from Kelvin to Celsius, you subtract 273.15 from the Kelvin value. The formula is quite simple: \( C = K - 273.15 \). So when you have a body temperature of \(310 K\), applying this formula gives you \( C = 310K - 273.15 = 36.85^{\textdegree}C \). This means that the average normal body temperature in Celsius is about \(36.85^{\textdegree}C\), which is close to the commonly cited \(37^{\textdegree}C\).

When dealing with temperature changes or differences, the degree of change is the same in Kelvin as in Celsius. This is because both scales increase at the same rate: a one-degree increase in Celsius corresponds to a one-degree increase in Kelvin.

Celsius to Fahrenheit Conversion

When converting temperatures from Celsius to Fahrenheit, which is common in countries like the United States, the formula to use is \( F = \frac{9}{5}C + 32 \). Knowing this formula allows you to grasp the temperature readings in a format you might be more familiar with.

For instance, the vigorous body temperature of \(40^{\textdegree}C\) would be converted to Fahrenheit by multiplying the Celsius temperature by \(\frac{9}{5}\) and then adding 32: \( F = \frac{9}{5}(40) + 32 = 104^{\textdegree}F \).

Similarly, for a body temperature that can lead to heat stroke at \(105^{\textdegree}F\), you can convert it back to Celsius using the inverse formula \( C = \frac{5}{9}(F - 32) \). Applied to this situation: \( C = \frac{5}{9}(105 - 32) = 40.56^{\textdegree}C \). Temperature conversions like these are practical not only in scientific settings but also in cooking, travel, and many other aspects of life.

Body Temperature Regulation

Body temperature regulation is a vital aspect of human physiology. It's the process by which our bodies maintain a stable internal temperature despite changes in the external environment. This temperature is generally around \(36.5^{\textdegree}C\) to \(37.5^{\textdegree}C\), or \(310 K\) on the Kelvin scale. The human body has several mechanisms in place to regulate temperature, including perspiration, shivering, expanding or constricting blood vessels, and metabolic adjustments.

During exercise, the body temperature can rise significantly, typically to about \(40^{\textdegree}C\) or \(313.15 K\), because of the increased metabolic rate. If body temperature rises above \(105^{\textdegree}F\) (\(40.56^{\textdegree}C\) or \(313.71 K\)), it could lead to heat stroke, a severe medical emergency requiring immediate attention.

The understanding of body temperature regulation is not only important for staying healthy but also for understanding the conditions under which the human body performs optimally.

Temperature Scales in Physics

In physics, understanding different temperature scales is essential. The primary scales are Celsius, Fahrenheit, and Kelvin. Each scale has its own uses, applications, and conversion formulas.

The Celsius scale is based on the properties of water, with \(0^{\textdegree}C\) being the freezing point of water and \(100^{\textdegree}C\) as its boiling point at standard atmospheric pressure. Fahrenheit, on the other hand, has its points of reference determined by a combination of various factors, and the freezing point of water is \(32^{\textdegree}F\), with the boiling point at \(212^{\textdegree}F\).

Kelvin is the scale used most in scientific measurements because it is an absolute temperature scale with its zero point at absolute zero, where theoretically no more thermal energy can be removed from a system.

In physics, temperatures are often measured in Kelvin for consistency and because it simplifies many physical laws, removing negative numbers from equations involving thermodynamics and kinetics.