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Make the following conversions: (a) \(62^{\circ} \mathrm{F}\) to \({ }^{\circ} \mathrm{C}\), (b) \(216.7\) \({ }^{\circ} \mathrm{C}\) to \({ }^{\circ} \mathrm{F}\), (c) \(233^{\circ} \mathrm{C}\) to \(\mathrm{K}\), (d) \(315 \mathrm{~K}\) to \({ }^{\circ} \mathrm{F}\), (e) \(2500^{\circ} \mathrm{F}\) to \(\mathrm{K}\).

Short Answer

Expert verified
(a) \(16.67^{\circ}C\), (b) \(454.04^{\circ}F\), (c) \(506.15K\), (d) \(139.33^{\circ}F\), (e) \(1644.26K\)

Step by step solution

01

(a) Convert 62°F to °C

Using the formula for converting Fahrenheit to Celsius: \(C = \frac{5(F - 32)}{9}\) \(C = \frac{5(62 - 32)}{9}\) \(C = \frac{150}{9}\) \(C \approx 16.67^{\circ}C\)
02

(b) Convert 216.7°C to °F

Using the formula for converting Celsius to Fahrenheit: \(F = \frac{9C}{5} + 32\) \(F = \frac{9(216.7)}{5} + 32\) \(F = 422.04 + 32\) \(F \approx 454.04^{\circ}F\)
03

(c) Convert 233°C to K

Using the formula for converting Celsius to Kelvin: \(K = C + 273.15\) \(K = 233 + 273.15\) \(K = 506.15K\)
04

(d) Convert 315 K to °F

First convert Kelvin to Celsius: \(C = K - 273.15\) \(C = 315 - 273.15\) \(C = 41.85^{\circ}C\) Now convert Celsius to Fahrenheit: \(F = \frac{9C}{5} + 32\) \(F = \frac{9(41.85)}{5} + 32\) \(F = 107.33 + 32\) \(F \approx 139.33^{\circ}F\)
05

(e) Convert 2500°F to K

First convert Fahrenheit to Celsius: \(C = \frac{5(F - 32)}{9}\) \(C = \frac{5(2500 - 32)}{9}\) \(C = \frac{12,340}{9}\) \(C \approx 1371.11^{\circ}C\) Now convert Celsius to Kelvin: \(K = C + 273.15\) \(K = 1371.11 + 273.15\) \(K = 1644.26K\)

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Key Concepts

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

Fahrenheit to Celsius
To convert temperatures from Fahrenheit to Celsius, you can use a simple mathematical formula. This formula helps you figure out what the temperature is in Celsius when you know it in Fahrenheit. The formula is: \[ C = \frac{5}{9}(F - 32) \] Here is how it works:
  • Subtract 32 from the Fahrenheit temperature. This adjustment accounts for the fact that the Fahrenheit scale doesn’t start at zero like the Celsius scale.
  • Multiply the result by 5. This step starts to bring the Fahrenheit number closer to its Celsius counterpart.
  • Divide by 9 to finalize the conversion, scaling the number down to a Celsius value.
For example, converting 62°F results in approximately 16.67°C. Therefore, to change Fahrenheit to Celsius, the major steps are subtracting, multiplying, and dividing. Simple and straightforward!
It’s essential for students to practice this with different numbers to feel comfortable with the conversion process.
Celsius to Fahrenheit
Converting Celsius to Fahrenheit is another essential skill. This conversion is very similar to the previous one, but it involves a few different steps. The formula used is quite straightforward: \[ F = \frac{9}{5}C + 32 \] To perform the conversion:
  • First, multiply the Celsius temperature by 9. This helps transition from the smaller range of Celsius to the larger range of Fahrenheit.
  • Then, divide the result by 5. This scaling down adjusts for the different step sizes of the degrees.
  • Finally, add 32. This offset accounts for the starting points of the different scales—Fahrenheit starting at 32 for freezing.
If you use this method with 216.7°C, you’ll determine it equates to approximately 454.04°F. Practicing with various temperatures will help students understand how these calculations reflect real-world temperature differences.
Celsius to Kelvin
Switching from Celsius to Kelvin is one of the simplest temperature conversions because it involves merely adding a constant. The formula is: \[ K = C + 273.15 \] Here's what you need to do:
  • Simply add 273.15 to the Celsius measurement. No multiplication or division is involved!
This simple addition shifts the starting point from the Celsius scale (where water freezes at 0°C) to the Kelvin scale (where absolute zero is 0 K). For instance, converting 233°C to Kelvin gives 506.15 K.
Since Kelvin is the absolute temperature scale used in scientific contexts, understanding this conversion is crucial in advanced studies.
Kelvin to Fahrenheit
Converting Kelvin directly to Fahrenheit is a bit more complex because it involves two steps. First, Kelvin is converted to Celsius, and then Celsius to Fahrenheit. Follow these steps: 1. **Convert Kelvin to Celsius**: Use the formula: \[ C = K - 273.15 \] Subtract 273.15 from the Kelvin temperature to find Celsius. For instance, with 315 K, this results in 41.85°C.2. **Convert Celsius to Fahrenheit**: Now, apply the formula: \[ F = \frac{9}{5}C + 32 \] Converting 41.85°C yields roughly 139.33°F. Converting temperatures this way helps develop a better understanding of how absolute temperatures relate to everyday scales. Each step involves fundamental math, reinforcing multiplication, division, addition, and subtraction skills. Remember to do the steps in order, as mixing them up can lead to errors in your final results.

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Most popular questions from this chapter

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