Suppose that a new temperature scale has been devised on which the melting point of ethanol (-117.3â°c and the boiling point of ethanol (78.3â°c) are taken as oos and 100â°s, respectively, where s is the symbol for the new temperature scale. derive an equation relating a reading on this scale to a reading on the celsius scale. what would this thermometer read at 25â°c?

See explanation below

Explanation:

In this case, let's form the equation into something similar to the known equations of temperature, for example:

°F = 9/5°C + 32 (1)

°K = °C + 273 (2)

As you can see, in both equations we need to add something to the celsius grade. We cannot use the equation of °K because if you make the difference between the new scale and the °C for both melting and boiling points, the result do not match. Let's suppose we say that

°S = °C + 117.3 °C

When you apply this formula to the boiling point, the result is not matching the given point of 100, so, let's put it as the equation of Farenheit:

°S = x°C + y (3)

Where "x" and "y" will be the numbers that will be added to the °C to convert it to the new scale of S.

We apply this formula to both melting and boiling point, and solve for x and y:

For melting:

0 = -117.3x + y

y = 117.3x (4)

Now, for boiling, we replace (4):

100 = 78.3x + y

100 = 78.3x + 117.3x

100 = 195.6x

x = 100/195.6

x = 0.5112

Now, let's replace this value to get "y":

y = 117.3 * 0.5112

y = 59.97 and we can round it to 60

Now, let's confirm this data match the given data (or really near):

°S = 0.5112 * (-117.3) + 60

°S = -59.97 + 60

°S = 0.03 °C

This result match the given m.p. of ethanol in the new scale (Remember that we round the value of y to a round number)

Therefore the new equation would be:

°S = 0.5112°C + 60

Now, 25°C in the new scale would be:

°S = 0.5112*25 + 60

°S = 72.78 °S

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