Question

Consider a new temperature scale (ºa) based on the melting and boiling points of ammonia (nh3) which are taken as 0.0 ºa and 100.0 ºa, respectively. On the celsius scale ammonia melts at –77.7 ºc and boils at –33.3 ºc. Find the temperature in ºa that corresponds to 25.0 ºc

Answer 1

Answer:-  25.0 degree C corresponds to 231 $^0A$ .

Solution:- Let's say the two temperature scales have linear relationship. The equation of line is:

$y=mx+c$

where, m is the slope of the line and c is the intercept.  Let's take the new temperature scale, $^0A$ for y and $^0C$ as $x$ . The equation would be looking as:

$^0A=m*^0C+c$

melting point of ammonia in new scale is 0.0 $^0A$ and in celsius scale it is -77.7 degree C. Boiling point in new scale is 100.0 $^0A$ and in celsius scale it is -33.3 degree C.

Let's plug in the values in the equation of line for melting points and boiling points to make two equations that we would solve:

For melting point:-  $0.0=m(-77.7)+c$              

For boiling point:- $100=m(-33.3)+c$

Now, we solve these two equations to find out the slope of the equation that is the value of m. Let's multiply the second equation by negative means changing all the signs from negative to positive and vice versa.

$0.0=m(-77.7)+c$  

$-100=m(+33.3)-c$

---------------------------------------------

$-100=-44.4m$

$m=\frac{-100}{-44.4}$

$m=2.25$

Let's plug in this value of m in any of the two equations we have for melting point and boiling points to find out the value of intercept, c.

Let's say we use $0.0=m(-77.7)+c$  equation.

$0.0=2.25(-77.7)+c$  

$0.0=-174.825+c$

$c=174.825$

Now, the first equation, $^0A=m*^0C+c$ could be written as:

$^0A=2.25*^0C+174.825$

We use this equation to convert the temperature of one scale to another.

We are asked to find the temperature in $^0A$ that corresponds to 25.0 $^0C$ .

Let's plug in the value of this degree C temperature in the above equation:

$^0A=2.25(25.0)+174.825$

= $^0A=56.25+174.825$

= $^0A=231.075$

This could be round to 231.

So, 25.0 degree C corresponds to 231 $^0A$ .