Suppose you were dissatisfied with both Celsius and Fahrenheit units and wanted to design your own temperature scale based on ethyl alcohol (ethanol). On the Celsius scale, ethanol has a melting point of -117.3 °C and a boiling point of 78.5 °C, but on your new scale calibrated in units of degrees ethanol, °E, you define ethanol to melt at 0 °E and boil at 200 °E. (e) If the outside thermometer reads 130 °E, how would you dress to go out?

Video transcript

Hi everyone. This problem reads suppose you wanted to create your own temperature scale based on proposed alcohol. Since you are unsatisfied with both the Celsius and Fahrenheit units, the melting point and boiling point of propane all on the Celsius scale are negative 126 degrees Celsius and 97.2 degrees Celsius, respectively. In the new scale, you define the melting point and boiling point of propane all at zero degrees P and 100 and 50 degrees P respectively. If the outside thermometer reads 99 degrees p, what would you wear to go out? Okay, So we know that the outside thermometer reads 99°P. So we're trying to determine what do we need to wear when we go outside. So let's go ahead and start off with what we're given in terms of propane all's boiling point and melting point. Okay, so let's start there. So we're right, propane all boiling point and propane all melting point. Okay, And the problem, we're told that the boiling point is 97.2 degrees Celsius and the melting point is negative 194. degrees Celsius. So, these are given in Celsius, we know that we have the two scales we're using because we're told that we are in both the Fahrenheit and dissatisfied with both the Celsius and Fahrenheit units. So let's go ahead and figure out what these temperatures are in degrees Celsius, I mean in degrees Fahrenheit, excuse me. So, to find the boiling point in degrees Fahrenheit, we're going to take the temperature and degrees Celsius. So 97.2 degrees Celsius. And we're going to multiply that by 9/5 plus 32. So this gives us a temperature of 206. degrees Fahrenheit. Okay, so let's go ahead and write that here. So the boiling point of propane ought in degrees Fahrenheit is 206.96 degrees Fahrenheit. So let's go ahead and do the same thing. But for the melting point in degrees Fahrenheit. So we're going to take the degrees in Celsius, so negative 194.8 degrees Celsius multiply that by 9/5 plus this gives us a temperature of 100 negative 194 point eight F. So now we know our melting point and boiling point in both degrees Celsius and Fahrenheit. Alright, so now we need to write out what were given in terms of the new scale, which is our degrees and P So for poor panels boiling point, we're told that on the new scale it's 100 and 50 degrees P and the melting point on the new scale is zero degrees P. Alright, so now we know what all of our units are are degree Celsius degrees Fahrenheit and our new scale. So we're going to use the boiling point and melting point of propane all and degrees P and Fahrenheit. Okay, so we're going to take the boiling point, let's write this in a different color. So we're going to take the boiling point and degrees Fahrenheit minus the melting point and degrees Fahrenheit and divide this by the boiling point and degrees P minus the melting point and degrees P. Okay, this is because we want the we want our units and degrees Fahrenheit per degree P. Okay, so let's go ahead and plug in our units. So we have 206.96 degrees Fahrenheit minus negative 194.8 degrees Fahrenheit over 150 degrees p minus zero degrees P. So this gives us an answer of 2.6784 degrees Fahrenheit over degrees P. So now that we have this, we can convert our degrees P two F and this will tell us what our degree, what our temperature is in Fahrenheit. So we can determine what we're going to wear outside. So now we're going to convert degrees P two F. Okay, so the way that we're going to do that is we're going to take our degrees Fahrenheit is going to equal degrees p times What we just saw. four, over degrees P plus -194.8. Okay. And we know what our degrees P is. So we can go ahead and plug that in, we know that our degrees P. On the new scale. Well, they tell us in the problem if the outside thermometer reads 99 degrees P. So we're going to plug that 99 here, so 99 degrees p. Times. So here you see rps are going to cancel Times 2. plus negative 194.8 is going to give us our degrees in Fahrenheit. And when we solve, we get 70.36 degrees Fahrenheit. So that's going to be our temperature. If it's 70.36 degrees Fahrenheit, we can wear jeans, cardigans, a T shirt and light sweaters. Okay, so our answer is if the outside thermometer reads 99 degrees P, which we converted two F, we know we would wear a cardigan t shirt and jeans. Okay? And we're gonna right here that if the thermometer reads 99°P so 99 degrees P equals cardigan t shirt and jeans. So we'll go ahead and highlight this as our final answer. And that is it for this problem? I hope this was helpful