Answer:
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:
<em>°S = x°C + y (3)</em>
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:
<u><em>°S = 0.5112°C + 60</em></u>
Now, 25°C in the new scale would be:
°S = 0.5112*25 + 60
<u><em>°S = 72.78 °S</em></u>