Question

Carry out the indicated temperature conversions. a. \(175^{\circ} \mathrm{F}\) to kelvins b. \(255 \mathrm{K}\) to Celsius degrees c. \(-45^{\circ} \mathrm{F}\) to Celsius degrees d. \(125^{\circ} \mathrm{C}\) to Fahrenheit degrees

Short answer

a. \(175^{\circ}\mathrm{F}\) is approximately 352.59 K. b. \(255\mathrm{K}\) is approximately -18.15^{\circ}\mathrm{C}. c. \(-45^{\circ}\mathrm{F}\) is approximately -42.78^{\circ}\mathrm{C}. d. \(125^{\circ}\mathrm{C}\) is approximately \(289^{\circ}\mathrm{F}\).

Step-by-step solution

Convert Fahrenheit to Celsius

To convert Fahrenheit to Celsius, we use the formula: Celsius = \( \frac{5}{9}(Fahrenheit - 32) \). Plugging in the given temperature of \(175^{\circ}\mathrm{F}\): Celsius = \( \frac{5}{9}(175 - 32) \).

Calculate Celsius

Simplify the equation to find the temperature in Celsius: Celsius = \( \frac{5}{9}(143) \approx 79.44 ^{\circ}\mathrm{C} \).

Convert Celsius to Kelvin

To convert Celsius to Kelvin, we use the formula: Kelvin = Celsius + 273.15. Plugging in the temperature of \(79.44^{\circ}\mathrm{C}\): Kelvin = 79.44 + 273.15.

Calculate Kelvin

Simplify the equation to find the temperature in Kelvin: Kelvin = 352.59 K. So, \(175^{\circ}\mathrm{F}\) is approximately 352.59 K. b. Convert \(255\mathrm{K}\) to Celsius degrees

Convert Kelvin to Celsius

To convert Kelvin to Celsius, we use the formula: Celsius = Kelvin - 273.15. Plugging in the given temperature of \(255\mathrm{K}\): Celsius = 255 - 273.15.

Calculate Celsius

Simplify the equation to find the temperature in Celsius: Celsius = -18.15 ^{\circ}\mathrm{C}\(. So, \)255\mathrm{K}\( is approximately \)-18.15^{\circ}\mathrm{C}$. c. Convert \(-45^{\circ}\mathrm{F}\) to Celsius degrees

Convert Fahrenheit to Celsius

Use the same formula from part (a): Celsius = \( \frac{5}{9}(Fahrenheit - 32) \). Plugging in the given temperature of \(-45^{\circ}\mathrm{F}\): Celsius = \( \frac{5}{9}(-45 - 32) \).

Calculate Celsius

Simplify the equation to find the temperature in Celsius: Celsius = \( \frac{5}{9}(-77) \approx -42.78^{\circ}\mathrm{C} \). So, \(-45^{\circ}\mathrm{F}\) is approximately \(-42.78^{\circ}\mathrm{C}\). d. Convert \(125^{\circ}\mathrm{C}\) to Fahrenheit degrees

Convert Celsius to Fahrenheit

To convert Celsius to Fahrenheit, we use the formula: Fahrenheit = \( \frac{9}{5}(Celsius) + 32 \). Plugging in the given temperature of \(125^{\circ}\mathrm{C}\): Fahrenheit = \( \frac{9}{5}(125) + 32 \).

Calculate Fahrenheit

Simplify the equation to find the temperature in Fahrenheit: Fahrenheit = \(257 + 32 = 289^{\circ}\mathrm{F}\). So, \(125^{\circ}\mathrm{C}\) is approximately \(289^{\circ}\mathrm{F}\).

Key concepts

Celsius to Kelvin Conversion

Converting temperatures from Celsius to Kelvin is straightforward. This conversion is especially useful in scientific contexts because Kelvin is the SI unit for temperature. It's easy to convert Celsius to Kelvin:

• Add 273.15 to the Celsius temperature. This accounts for the difference in the starting point of each scale. Celsius starts at the freezing point of water, 0°C, and Kelvin starts at absolute zero, which is -273.15°C.

For example, if the temperature is 25°C, then in Kelvin it will be:\[ 25 + 273.15 = 298.15 \] Remember, the magnitude of a degree Celsius is the same as a Kelvin, so the numbers add up easily. This makes Kelvin useful in formulae that involve temperature ratios or differences.

Fahrenheit to Celsius Conversion

Converting from Fahrenheit to Celsius helps when you need to work with temperatures in more scientific and global contexts. The formula to change Fahrenheit into Celsius is:\[ \text{Celsius} = \frac{5}{9}(\text{Fahrenheit} - 32) \] This formula subtracts 32 to correct the offset between the two scales, then multiplies by \( \frac{5}{9} \) to adjust for the difference in degree size. When you want to convert 100°F to Celsius, use:\[ \text{Celsius} = \frac{5}{9}(100 - 32)\] Simplify this to:\[ \text{Celsius} = \frac{5}{9} \times 68 \approx 37.78^{\circ} \text{C} \] So, 100°F translates to approximately 37.78°C. This conversion is ideal for preparing to use scientific equations, since Celsius is part of the Metric System, commonly used worldwide.

Kelvin to Celsius Conversion

The Kelvin to Celsius conversion is just as simple. This conversion only requires subtracting a constant:\[ \text{Celsius} = \text{Kelvin} - 273.15 \] This constant accounts for the difference in starting points between the two scales. For instance, converting 300 Kelvin to Celsius:\[ 300 - 273.15 = 26.85^{\circ} \text{C} \] This indicates that 300 K is the same as 26.85°C. This method is particularly helpful in fields like chemistry or physics where Kelvin is typically used, but a Celsius understanding is necessary for practical lab work or environmental discussions.

Celsius to Fahrenheit Conversion

When changing Celsius into Fahrenheit, it's crucial for understanding weather conditions or recipes that use the Imperial System. The formula is:\[ \text{Fahrenheit} = \frac{9}{5}(\text{Celsius}) + 32 \] This ensures the scale aligns with Fahrenheit's degree size which is larger than Celsius. For example, converting 0°C to Fahrenheit would be:\[ \text{Fahrenheit} = \frac{9}{5}(0) + 32 \] Which simplifies to 32°F. To convert 20°C, the calculation would look like:\[ \text{Fahrenheit} = \frac{9}{5}(20) + 32 \]Simplify to:\[ \text{Fahrenheit} = 36 + 32 = 68^{\circ} \text{F} \] This conversion is useful for international travel or understanding cross-cultural temperature information easily.