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Dermatologists often remove small precancerous skin lesions by freezing them quickly with liquid nitrogen, which has a temperature of \(77 \mathrm{K}\). What is this temperature on the (a) Celsius and (b) Fahrenheit scales?

Short Answer

Expert verified
Liquid nitrogen at 77 K is -196.15°C or -321.07°F.

Step by step solution

01

Convert Kelvin to Celsius

To convert a temperature from Kelvin to Celsius, use the formula: \[ \text{Celsius} = \text{Kelvin} - 273.15 \].For this problem, substitute 77 for Kelvin:\[ \text{Celsius} = 77 - 273.15 = -196.15 \].Thus, the temperature in Celsius is \(-196.15\) degrees.
02

Convert Celsius to Fahrenheit

To convert from Celsius to Fahrenheit, use the formula: \[ \text{Fahrenheit} = \text{Celsius} \times \frac{9}{5} + 32 \].Using the temperature from Step 1, substitute \(-196.15\) for Celsius:\[ \text{Fahrenheit} = (-196.15) \times \frac{9}{5} + 32 \approx -321.07 \].Thus, the temperature in Fahrenheit is approximately \(-321.07\) degrees.

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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 temperature conversion is crucial in various scientific disciplines, particularly in physics and chemistry. The Kelvin to Celsius conversion is essential because Kelvin is often used in scientific contexts due to its absolute zero point, which is the lowest possible temperature. Kelvin does not use degrees, making its scale distinct. When converting Kelvin to Celsius, use the simple formula:
  • Celsius = Kelvin - 273.15
To illustrate, if liquid nitrogen is at a temperature of 77 Kelvin, converting it to Celsius involves just subtracting 273.15 from 77. This calculation results in -196.15 degrees Celsius.
This conversion helps provide a more familiar scale, as Celsius is commonly used in daily life and in many scientific applications.
Celsius to Fahrenheit conversion
Once the temperature is known in Celsius, converting it to Fahrenheit can be useful, especially in regions where Fahrenheit is the standard unit like the United States. The formula to switch from Celsius to Fahrenheit is:
  • Fahrenheit = Celsius \(\times \frac{9}{5} + 32\)
To continue from the previous section, we convert -196.15 degrees Celsius, which is obtained from the Kelvin to Celsius conversion, into Fahrenheit. Apply the formula step-by-step: first, multiply -196.15 by 9/5, which equals approximately -352.07. Then, add 32 to adjust for the offset in the Fahrenheit scale, resulting in approximately -321.07 degrees Fahrenheit.
This temperature scale conversion is necessary for communicating scientific data across different units, accommodating diverse regional preferences, and enhancing clarity in scientific discussions.
Unit conversion in physics
Unit conversions are fundamental in physics, ensuring scientific data is consistently and clearly interpreted worldwide. Converting between temperature units, like Kelvin to Celsius to Fahrenheit, reflects how different scales are interrelated and the need for standardizing scientific measurements.
Understanding these conversions helps in fields ranging from meteorology to engineering, where precise temperature measurements are critical.
Effective unit conversion allows scientists and engineers to:
  • Maintain accuracy in calculations.
  • Compare data collected under different scales.
  • Ensure agreement between experimental outcomes and theoretical predictions.
Temperature is just one unit of many that often require conversion, underlining the need for a robust grasp of conversion techniques in any scientific endeavor.
Always remember, each pair of units will have its specific conversion formula, so familiarity with these can significantly enhance topic comprehension.

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Most popular questions from this chapter

A 42 -kg block of ice at \(0^{\circ} \mathrm{C}\) is sliding on a horizontal surface. The initial speed of the ice is \(7.3 \mathrm{m} / \mathrm{s}\) and the final speed is \(3.5 \mathrm{m} / \mathrm{s} .\) Assume that the part of the block that melts has a very small mass and that all the heat generated by kinetic friction goes into the block of ice. Determine the mass of ice that melts into water at \(0^{\circ} \mathrm{C}\).

One ounce of a well-known breakfast cereal contains 110 Calories (1 food Calorie \(=4186 \mathrm{J}\) ). If \(2.0 \%\) of this energy could be converted by a weight lifter's body into work done in lifting a barbell, what is the heaviest barbell that could be lifted a distance of \(2.1 \mathrm{m} ?\)

One January morning in \(1943,\) a warm chinook wind rapidly raised the temperature in Spearfish, South Dakota, from below freezing to \(+12.0^{\circ} \mathrm{C}\). As the chinook died away, the temperature fell to \(-20.0^{\circ} \mathrm{C}\) in 27.0 minutes. Suppose that a \(19-\mathrm{m}\) aluminum flagpole were subjected to this temperature change. Find the average speed at which its height would decrease, assuming the flagpole responded instantaneously to the changing temperature.

When resting, a person has a metabolic rate of about \(3.0 \times\) \(10^{5}\) joules per hour. The person is submerged neck-deep into a tub containing \(1.2 \times 10^{3} \mathrm{kg}\) of water at \(21.00^{\circ} \mathrm{C} .\) If the heat from the person goes only into the water, find the water temperature after half an hour.

If a nonhuman civilization were to develop on Saturn's largest moon, Titan, its scientists might well devise a temperature scale based on the properties of methane, which is much more abundant on the surface than water is. Methane freezes at \(-182.6^{\circ} \mathrm{C}\) on Titan, and boils at \(-155.2^{\circ} \mathrm{C}\) Taking the boiling point of methane as \(100.0^{\circ} \mathrm{M}\) (degrees Methane) and its freezing point as \(0^{\circ} \mathrm{M},\) what temperature on the Methane scale corresponds to the absolute zero point of the Kelvin scale?

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