Question

( \(a\) ) The temperature of the surface of the Sun is about 6000 \(\mathrm{K}\). Express this on the Fahrenheit scale. (b) Express normal human body temperature, \(98.6^{\circ} \mathrm{F}\) on the Celsius scale. ( \(c\) ) In the continental United States, the lowest officially recorded temperature is \(-70^{\circ} \mathrm{F}\) at Rogers Pass, Montana. Express this on the Celsius scale. ( \(d\) ) Express the normal boiling point of oxygen, \(-183^{\circ} \mathrm{C}\), on the Fahrenheit scale. ( \(e\) ) At what Celsius temperature would you find a room to be uncomfortably warm?

Short answer

The temperature of the Sun's surface is approximately \(10,232^{\circ} F\). The human body temperature is around \(37^{\circ} C\). The temperature at Rogers Pass, Montana is about \(-56.67^{\circ} C\). The boiling point of oxygen is approximately \(-297.4^{\circ} F\). A room temperature above \(32^{\circ} C\) is generally considered uncomfortably warm.

Step-by-step solution

Convert from Kelvin to Fahrenheit

To convert from Kelvin to Fahrenheit, we use the formula \[ F = 9/5(K - 273.15) + 32\]. Plug in \(K = 6000\) and calculate the result.

Convert from Fahrenheit to Celsius

To convert from Fahrenheit to Celsius, we use the formula \[ C = 5/9(F - 32)\]. Plug in \(F = 98.6\) and calculate the result.

Convert from Fahrenheit to Celsius

Again, we use the formula \[ C = 5/9(F - 32)\]. This time, plug in \(F = -70\) and calculate the result.

Convert from Celsius to Fahrenheit

To convert from Celsius to Fahrenheit, we can use the formula \[ F = 9/5C + 32\]. Plug in \(C = -183\) and calculate the result.

Find Uncomfortably Warm Temperature in Celsius

The answer to this would vary based on individual preferences. However, as a general guideline, any room temperature above \(32^{\circ} C\) (about \(90^{\circ} F\) on the Fahrenheit scale) is typically considered to be uncomfortably warm for most people.

Key concepts

Kelvin to Fahrenheit Conversion

Converting temperatures from the Kelvin scale to the Fahrenheit scale is a common task in thermal physics, particularly for understanding extreme temperatures such as those on the surface of the sun or in space. The formula for this conversion is \[ F = \frac{9}{5}(K - 273.15) + 32 \]. To put it simply, one must subtract 273.15 from the Kelvin temperature, multiply the result by 9/5, and then add 32 to arrive at the temperature in Fahrenheit.

For example, to convert 6000 Kelvin – the approximate surface temperature of the Sun, the calculation is as follows:
\[ F = \frac{9}{5}(6000K - 273.15) + 32 \approx 10292^\circ F \]. Therefore, 6000 Kelvin is equivalent to approximately 10292 degrees Fahrenheit.

Fahrenheit to Celsius Conversion

The counterpart to the previous conversion is changing Fahrenheit temperatures to Celsius. This is especially useful in daily life, as the Celsius scale is widely used around the world. The conversion formula is \[ C = \frac{5}{9}(F - 32) \]. Starting with the Fahrenheit temperature, you subtract 32, then multiply this by 5/9.

Converting normal human body temperature from Fahrenheit to Celsius, we have \(98.6^\circ F\), and using the formula provided: \[ C = \frac{5}{9}(98.6 - 32) \approx 37^\circ C \]. Thus, the normal body temperature of 98.6 degrees Fahrenheit is about 37 degrees Celsius. This conversion is significant in medicine and environmental studies.

Thermal Physics

Thermal physics is the study of heat energy, temperature, and their effects on matter. It encompasses concepts such as thermal equilibrium, heat transfer, and the kinetic theory of gases. Temperature is a measure of the thermal energy within a substance, with higher temperatures indicating more thermal energy.

In thermal physics, we learn that heat always flows from warmer to cooler substances until thermal equilibrium is reached. Key concepts also include the various methods of heat transfer: conduction, convection, and radiation. Understanding these fundamentals allows us to apply thermal physics in various scientific and engineering contexts, including climate studies and materials science.

State Changes in Matter

Matter can exist in several distinct states, primarily solid, liquid, and gas. The changes between these states—melting, freezing, vaporization, condensation, sublimation, and deposition—are termed phase transitions. These transitions are driven by thermal energy.

When a substance gains or loses heat, it may undergo a phase change. For instance, increasing the thermal energy of a solid can cause it to melt into a liquid. Each substance has specific temperatures at which these changes occur, known as melting points and boiling points. The control and understanding of these state changes have practical applications in a wide array of fields, from meteorology to culinary arts.