You are watching: At what temperature do the fahrenheit and celsius scales have the same numerical value?
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This is College Physics Answers through Shaun Dychko. In part A of this question we"re going to figure out at what numerical number carry out we have the temperature in levels Celsius being the exact same as the temperature in levels Fahrenheit. So here"s our convariation between Fahrenheit and Celsius and also we"re going to say that the Fahrenheit temperature and the Celsius temperature check out the specific very same number which we"ll contact X. So replace temperature in levels Fahrenheit and also temperature in degrees Celsius replace both those temperatures with the letter X and currently we"ll settle for X. So we"ll subtract 9 over 5 X from both sides and we end up via X minus 9 over 5 X equals 32. Factor out the widespread element X and also we have X times bracket 1 minus 9 over 5 amounts to 32. And 1 minus 9 over 5 is negative 4 over 5 bereason this one can be multiplied by 5 over 5 to acquire a common denominator. So 5 minus 9 is negative 4 and also all created over 5. And then multiply both sides by negative 5 over 4 and also we obtain X is negative 5 times 32 over 4 which is negative 40. So the temperature at which the Fahrenheit scale and also the Celsius range review the exact same number is at negative 40 degrees Fahrenheit or you can say negative 40 levels Celsius. And then Part B asks for the exact same question comparing temperature in degrees Fahrenheit to temperature in Kelvin. So utilizing this formula up below replacing the temperature in degree Celsius through this formula here for the temperature expressed in Kelvin. And so to convert from Kelvin right into Celsius you subtract 273.15. So we"re going to substitute this in location of temperature in degrees Celsius in this formula below. So this component gained reput by this so that we have actually temperature in Kelvin here. So the temperature in Kelvin and also the temperature in levels Fahrenheit are expected to be the very same number which we"ll speak to X aobtain and also then replacing both these temperatures with letter X. And now we distribute the 9/5s right into the bracket. So we have X equals 9 over 5X minus 273.15 times 9 over 5 plus 32. This continuous term works out to negative 459.67. And then we also subtract 9 over 5 X from both sides and also then factor out the widespread element X below. And we have X times 1 minus 9 over 5 equates to negative 459.67. 1 minus 9 over 5 becomes negative 4 over 5. Multiply both sides by negative 5 over 4 and also we obtain negative 5 over 4 times negative 459.67 is 575. So once the temperature is 575 Kelvin or 575 levels Fahrenheit we gain the very same number from these two different temperature scales.
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