Question

The temperature of ambient air in a certain location is measured to be \(-40^{\circ} \mathrm{C}\). Express this temperature in Fahrenheit \(\left(^{\circ} \mathrm{F}\right),\) Kelvin \((\mathrm{K}),\) and Rankine \((\mathrm{R})\) units.

Short answer

Question: Convert the given temperature of -40°C to Fahrenheit, Kelvin, and Rankine. Answer: The temperature of -40°C can be converted to the following: - Fahrenheit: -40°F - Kelvin: 233.15 K - Rankine: 419.67 R

Step-by-step solution

Convert Celsius to Fahrenheit

To convert the given Celsius temperature to Fahrenheit, we will use the formula: \(^{\circ}\mathrm{F} = \frac{9}{5}\,^{\circ}\mathrm{C} + 32\). Plugging in the given temperature, we get: $$ ^{\circ}\mathrm{F} = \frac{9}{5} \times (-40) + 32 $$ Now, simplify the expression: $$ ^{\circ}\mathrm{F} = -72 + 32 = -40 $$ So the temperature in Fahrenheit is \(-40^{\circ}\mathrm{F}\).

Convert Celsius to Kelvin

To convert the given Celsius temperature to Kelvin, we will use the formula: \(\mathrm{K} = \,^{\circ}\mathrm{C} + 273.15\). Plugging in the given temperature, we get: $$ \mathrm{K} = -40 + 273.15 $$ Now, simplify the expression: $$ \mathrm{K} = 233.15 $$ So the temperature in Kelvin is \(233.15 \mathrm{K}\).

Convert Celsius to Rankine

To convert the given Celsius temperature to Rankine, we will use the formula: \(\mathrm{R} = \frac{9}{5}\,^{\circ}\mathrm{C} + 491.67\). Plugging in the given temperature, we get: $$ \mathrm{R} = \frac{9}{5} \times (-40) + 491.67 $$ Now, simplify the expression: $$ \mathrm{R} = -72 + 491.67 = 419.67 $$ So the temperature in Rankine is \(419.67 \mathrm{R}\). In conclusion, the temperature of \(-40^{\circ}\mathrm{C}\) can be expressed as following: - Fahrenheit: \(-40^{\circ}\mathrm{F}\) - Kelvin: \(233.15 \mathrm{K}\) - Rankine: \(419.67 \mathrm{R}\)