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Suppose you wanted to design your own temperature scale based on methyl alcohol
(methanol). On the Celsius scale, methanol has a melting point of −96 ◦C and a boiling
point of 64 ◦C, but on your new scale calibrated in units of degrees methanol, ◦M, you
define methanol to melt at 0◦M and boil at 200◦M. On the methanol scale, the melting
and boiling points of water are?

 

I know the answer. But how can I get the answer?????

Asked by zrinidhi3 10th April 2018, 9:20 AM
Answered by Expert
Answer:
Consider temperature scales °M and °C are linear 
We know, the equation of line is given by y= mx+b
where, m- slope of line
b- intercept of line
Therefore, equation which converts celcius scale to methanol will be 
°M = m°C+b...(1)
Now we are given the temperatures for methanol in Celcius and methanol scale
they are as follows:
               
  °C °M
Melting Point -96 0
Boiling Point 64 200
 
Now we need to derive the formula for converting Celcius to methanol scale 
Therefore by substituting the values in eqaution (1) we get,
For melting point of methanol,
0= m(-96)+b...(2)
and 
For boiling point of methanol,
200=m(64)+b...(3)
Solving these two equations simultaneaously we get,
 
   200=  64m+b
-]    0= -96m+b
_______________
  m equals 5 over 4 equals space 1.25
and by substituting m in equation (3),
b= 120
 
Thus eqaution (1) can be written as,
°M = 1.25°C+120...(4)
 
Melting and Boiling point of water is 0°C and 100°C respectively.
Now substitute this in equation (4) and we get,
 
Melting point of water is 
°M = 1.25(0) +120= 120°M
And Boiling point of water is 
°M = 1.25(100) +120= 125+120= 245°M
Answered by Expert 10th April 2018, 11:44 AM
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