Question # On a new scale of temperature (which is linear) and called the ( W ) scale, the freezing and boiling points of water are ( 39^{circ} mathrm{W} ) mol ( 239^{circ} mathrm{W} ) respectively. What will be the temperature on the new scale, corresponding to a temperature of ( 39^{circ} mathrm{C} ) on the Celsius scale?

# On a new scale of temperature (which is linear) and called the ( W ) scale, the freezing and boiling points of water are ( 39^{circ} mathrm{W} ) mol ( 239^{circ} mathrm{W} ) respectively. What will be the temperature on the new scale, corresponding to a temperature of ( 39^{circ} mathrm{C} ) on the Celsius scale?

1 ( 78^{circ} mathrm{W} )

2. (117^{circ} mathrm{W} )

3. (200^{circ} mathrm{W} )

4. ( 139^{circ} mathrm{W} )

Solution

B. ( 117^{circ} mathrm{C} )

In general, whenever we are to go from any known scale to any unknown scale, then we follow the equation

(temperature on known scale) - (LFP for known scale)

(UFP - LFP ) Known (temerature on unknown scale)

( =-( ) LEP for unknown scale ( ) )

(UFP-LFP) unknown

or ( frac{390-0}{100-0}=frac{t-39}{239-39} )

( t=117^{circ} mathrm{W} )

LFP = Lower fixed point UFP = Upper fixed point