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A tungsten light bulb filament may operate at 2900 K. What is its Fahrenheit temperature? What is this on the Celsius scale?

Short Answer

Expert verified
The temperature of the filament is 2626.85 °C, and 4756.33 °F.

Step by step solution

01

Convert Kelvin to Celsius

To convert Kelvin to Celsius, use the formula: Celsius temperature \( C = K - 273.15 \). Plug in the Kelvin temperature and solve for Celsius.
02

Convert Celsius to Fahrenheit

To convert Celsius to Fahrenheit, use the formula: Fahrenheit temperature \( F = (C \times \frac{9}{5}) + 32 \). Substitute the Celsius temperature obtained from Step 1 into this formula to get the Fahrenheit temperature.

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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 conversion between Kelvin and Celsius is fundamental in the field of physics and other sciences. The Kelvin scale is an absolute thermodynamic temperature scale where zero on the scale, 0 K, is defined as absolute zero—the point at which theoretical molecular energy is minimal.

To convert a temperature from Kelvin (K) to Celsius (C), you can use the following simple formula: \[ C = K - 273.15 \].
For instance, if you have a temperature of 2900 K that you need to convert to Celsius, you subtract 273.15 from 2900, resulting in a Celsius temperature of approximately 2626.85 C. Remember, while Kelvin is based on an absolute scale, Celsius is a relative scale where 0 C is the freezing point of water. This conceptual difference is crucial because it informs why we cannot simply equate the two units without converting.
Celsius to Fahrenheit Conversion
The Celsius to Fahrenheit conversion is useful in daily life, especially living in regions where the Fahrenheit scale is preferred. Unlike the direct subtraction used in Kelvin to Celsius conversions, converting from Celsius to Fahrenheit involves scaling and then shifting the temperature value.

The formula to convert Celsius (C) to Fahrenheit (F) is given by: \[ F = (C \times \frac{9}{5}) + 32 \].
If we take the Celsius temperature from our previous example, 2626.85 C, to find the Fahrenheit temperature, you multiply the Celsius temperature by 9/5 and then add 32. Thus, the Fahrenheit temperature would be \[ (2626.85 \times \frac{9}{5}) + 32 \approx 4756.33 \] F.
This formula shows that the temperature scales increase at different rates because of the different intervals defined for the freezing and boiling points of water on the two scales.
Thermodynamic Temperature Scales
Thermodynamic temperature scales are crucial in providing universal standards for measuring temperature. The Kelvin scale, the primary unit of temperature in the International System of Units (SI), is an absolute temperature scale rooted in the fundamental laws of thermodynamics.

On the opposite end of the temperature spectrum is absolute zero, the point on the Kelvin scale at which no more thermal energy can be removed from a system. This concept is pivotal to understanding the thermodynamic temperature scales because it establishes a solid foundation from which all thermal energy can be measured.

While Celsius and Fahrenheit are widely used for everyday weather temperature measurements and cooking, Kelvin is used extensively in scientific research and calculations. The different scales emphasize how we measure and interact with thermal energy and the importance of standardized units for scientific communication.

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Most popular questions from this chapter

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of \(1.40 \times 10^{7} \mathrm{N} / \mathrm{m}^{2}\) and a temperature of \(25.0^{\circ} \mathrm{C} .\) Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature \(\left(-78.5^{\circ} \mathrm{C}\right)\) to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? (b) What is the final pressure if one-tenth of the gas escapes? (c) To what temperature must the tank be cooled to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)? (d) Does cooling the tank appear to be a practical solution?

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Laser vision correction often uses an excimer laser that produces \(193-\mathrm{nm}\) electromagnetic radiation. This wavelength is extremely strongly absorbed by the cornea and ablates it in a manner that reshapes the cornea to correct vision defects. Explain how the strong absorption helps concentrate the energy in a thin layer and thus give greater accuracy in shaping the cornea. Also explain how this strong absorption limits damage to the lens and retina of the eye.

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