You are watching: At what temperature do the fahrenheit and celsius scales have the same numerical value?
This is college Physics Answers with Shaun Dychko. In component A of this inquiry we"re walk to number out at what numerical number carry out we have actually the temperature in levels Celsius being the same as the temperature in levels Fahrenheit. For this reason here"s ours conversion in between Fahrenheit and also Celsius and we"re going come say the the Fahrenheit temperature and also the Celsius temperature read the precise same number which we"ll contact X. So change temperature in levels Fahrenheit and also temperature in levels Celsius change both those temperatures through the letter X and also now we"ll deal with for X. Therefore we"ll subtract 9 over 5 X from both sides and we end up v X minus 9 over 5 X equals 32. Variable out the common factor X and also we have actually X time bracket 1 minus 9 end 5 equals 32. And also 1 minus 9 end 5 is an unfavorable 4 end 5 since this one deserve to be multiplied by 5 end 5 to gain a typical denominator. So 5 minus 9 is an unfavorable 4 and also all created over 5. And also then main point both political parties by negative 5 end 4 and also we acquire X is an adverse 5 times 32 over 4 i m sorry is an unfavorable 40. So the temperature in ~ which the Fahrenheit scale and the Celsius scale check out the same number is at negative 40 levels Fahrenheit or you might say an unfavorable 40 degrees Celsius. And also then component B asks for the same inquiry comparing temperature in degrees Fahrenheit to temperature in Kelvin. So utilizing this formula up right here replacing the temperature in level Celsius v this formula here for the temperature expressed in Kelvin. And so to convert from Kelvin right into Celsius friend subtract 273.15. For this reason we"re walk to substitute this in place of temperature in degrees Celsius in this formula here. Therefore this part got changed by this so the we have actually temperature in Kelvin here. For this reason the temperature in Kelvin and the temperature in degrees Fahrenheit space meant to be the exact same number i beg your pardon we"ll speak to X again and also then replacing both this temperatures v letter X. And also now we distribute the 9/5s into the bracket. So we have X amounts to 9 over 5X minus 273.15 times 9 end 5 add to 32. This continuous term functions out to negative 459.67. And also then we also subtract 9 over 5 X from both sides and then aspect out the common factor X here. And also we have actually X time 1 minus 9 over 5 equals an unfavorable 459.67. 1 minus 9 over 5 becomes an adverse 4 end 5. Multiply both sides by an adverse 5 over 4 and we get an unfavorable 5 end 4 times negative 459.67 is 575. So when the temperature is 575 Kelvin or 575 degrees Fahrenheit we acquire the exact same number from this two different temperature scales.
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