On a new Jekyll temperature scale, water freezes at 17 °J and
boi...

Question

On a new Jekyll temperature scale, water freezes at 17 °J and
boils at 97 °J. On another new temperature scale, the Hyde
scale, water freezes at 0 °H and boils at 120 °H. If methyl alcohol
boils at 84 °H, what is its boiling point on the Jekyll scale?

Accepted Answer

Hi everyone for this problem, we're told that the freezing point of water was determined to be 15 degrees W. On the W scale and zero degrees V. On the V scale. In another experiment, the boiling point of water was determined to be 75 degrees W. On the W scale, and 100 and 10 degrees V. On the V scale. We're being asked that if ethanol boils at 40 degrees W, what is its boiling point on the V scale? So we have two experiments here and let's write this out so that we can see it. So we're told at 15°W. That's equal to 0° v. And at 75 degrees W. That is equal to 110° v. So this is our two experiments. And we can assume a linear relationship between these two temperatures and we can assume that linear relationship by using the formula for slope Y equals M X plus B. Okay, So what we can do here is we can solve for our slope. And what that's going to tell us is that our slope is going to equal the change in our W scale over the change in r. V scale. And so if we write out what we're given, we have our slope is equal to our change in our W scale is 75 degrees W minus 15 degrees W. And this is over our change and RV scale, Which is 100 and 10 degrees V minus zero degrees V. So when we solve that, we get a slope of Over 110. And this simplifies to six over 11. Okay, so what we can do with Y equals mx plus B. I'll move this over to the side here. What we can do with Y equals mx plus B. Is we can rearrange this or plug in what we know for our first um linear relationship and solve for B. So let's plug in what we know for our first linear relationship, which is this one. Okay, so we know that are why is 15? Our slope, which we just calculated is 6/11. R. X is zero plus B. So essentially will get B is equal to 15. Okay, so now we can use this equation, we have the equation why is equal to 6/11 times X plus 15. Okay, so this is our equation and this essentially translates to degrees W is equal to 6/11 times degrees v. Plus 15. So the question asks if ethanol boils at 40 degrees W what is its boiling point on the V scale? So at 40° on the W scale, we want to find our degrees V. Okay, so let's do that by saying our degrees W Is equal to 6/11 times our degree v. Plus 15. Now we're going to isolate this to solve for degrees V. And so we'll have degree W -15 Is equal to 6/ times degree v. And so then we get our degree V is equal to our degree W -15, divided by six Over 11. So now We're going to plug in 40 for this w right here. Okay, because we're told at 40°W. So let's do that and then we'll be done. So we have our degree V is equal to 40 Degree W -15, divided by 6/11. And this gives us a final answer of 45 0.83 degrees V. This is our final answer for this problem and this concludes this problem. I hope this was helpful.

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