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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 40°C to Kelvin

To convert Celsius to Kelvin, use the formula:\[ K = °C + 273.15 \]For \( 40^{\circ}C \):\[ K = 40 + 273.15 = 313.15 \, K \].

02

Convert 40°C to Fahrenheit

To convert Celsius to Fahrenheit, use the formula:\[ F = \left( \frac{9}{5} \times °C \right) + 32 \]For \( 40^{\circ}C \):\[ F = \left( \frac{9}{5} \times 40 \right) + 32 = 104^{\circ} \mathrm{F} \]

03

Express 7°C difference in Kelvins

The temperature difference in Celsius is equivalent to the difference in Kelvins. Thus, a difference of \( 7 \, C^{\circ} \) is also a difference of \( 7 \, K \).

04

Express 7°C difference in Fahrenheit

Use the formula for converting temperature differences from Celsius to Fahrenheit:\[ \Delta F = \frac{9}{5} \times \Delta C \]For \( 7 \, C^{\circ} \):\[ \Delta F = \frac{9}{5} \times 7 = 12.6^{\circ} \mathrm{F} \].

05

Convert 4°C to Fahrenheit and Kelvin

For Fahrenheit:\[ F = \left( \frac{9}{5} \times 4 \right) + 32 = 39.2^{\circ} \mathrm{F} \]For Kelvin:\[ K = 4 + 273.15 = 277.15 \, K \].

06

Convert -160°C to Fahrenheit and Kelvin

For Fahrenheit:\[ F = \left( \frac{9}{5} \times (-160) \right) + 32 = -256^{\circ} \mathrm{F} \]For Kelvin:\[ K = -160 + 273.15 = 113.15 \, K \].

07

Convert 105°F to Celsius

Use the formula to convert Fahrenheit to Celsius:\[ °C = \left( \frac{5}{9} \right) \times (F - 32) \]For \( 105^{\circ} \mathrm{F} \):\[ °C = \left( \frac{5}{9} \right) \times (105 - 32) = 40.6^{\circ} \mathrm{C} \].

08

Convert 105°F to Kelvin

Using the Celsius result from the previous step, convert to Kelvin:\[ K = 40.6 + 273.15 = 313.75 \, K \].

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Key Concepts

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

Celsius to Kelvin conversion

Converting Celsius to Kelvin is a straightforward process. It involves adding 273.15 to the Celsius temperature value. This conversion is crucial for many scientific calculations because Kelvin is the SI unit for temperature, widely used in science and engineering fields.
For example, if you have a temperature of \(40^{\circ}C\), to convert it to Kelvin, use the formula:
\[ K = °C + 273.15 \]
So, \(40^{\circ}C\) becomes \(313.15 K\).

• Ensures accurate measurement range in scientific contexts.
• Used in chemistry, physics, and many other sciences.

Fahrenheit to Celsius conversion

The conversion from Fahrenheit to Celsius is also common and necessary for a variety of applications, especially in daily weather forecasts or medical settings.
To convert from Fahrenheit to Celsius, the formula is:
\[ \text{°C} = \left( \frac{5}{9} \right) \times (F - 32) \]
For instance, if you have a temperature of \(105^{\circ} \mathrm{F}\), converting it to Celsius would result in \(40.6^{\circ} \mathrm{C}\).

• Useful for understanding temperatures in different countries.
• Essential for interpreting weather data across various regions.
• Helps in medical treatments and laboratory settings.

Temperature difference calculation

Calculating temperature differences is important when discussing changes in bodily or environmental conditions. When dealing with temperature differences, the conversion process becomes slightly different.
The temperature difference in Celsius directly corresponds to the difference in Kelvin. This means no conversion factor is needed; a difference of \(7^{\circ} \mathrm{C}\) is equivalent to a difference of \(7 \mathrm{K}\).
However, converting a temperature difference to Fahrenheit involves a factor:
\[ \Delta F = \frac{9}{5} \times \Delta C \]
In this case, a \(7^{\circ} \mathrm{C}\) difference equates to \(12.6^{\circ} \mathrm{F}\).

• Helps in understanding climatic shifts.
• Significant in medical diagnostics like fever evaluation.

Heat stroke temperature

Understanding heat stroke temperature is crucial for health and safety. Heat stroke is a serious condition when the body's temperature exceeds safe levels, usually \(105^{\circ} \mathrm{F}\) or higher.
Converting this to Celsius using the formula:
\[ \text{°C} = \left( \frac{5}{9} \right) \times (F - 32) \]
gives \(40.6^{\circ} \mathrm{C}\).
And to convert the Celsius value to Kelvin:
\[ K = 40.6 + 273.15 = 313.75 \mathrm{K} \]

• Crucial for preventing and responding to heat-related illnesses.
• Important to monitor during extreme heat conditions.

Blood storage temperature

Proper blood storage is vital for maintaining its usability for medical procedures. Blood storage temperatures vary depending on the duration and conditions.
For short-term storage, blood is kept at \(4^{\circ} \mathrm{C}\), which converts to:

• \(39.2^{\circ} \mathrm{F}\)
• \(277.15 \mathrm{K}\)

For long-term storage, temperature is lowered to \(-160^{\circ} \mathrm{C}\), converting to:

• \(-256^{\circ} \mathrm{F}\)
• \(113.15 \mathrm{K}\)

These conversions ensure that blood remains safe and usable for its intended medical purposes.