Question

if a certain thermometer scale indicates 105.6° and -25.0° has the upper and lower fixed point respectively, what would the scale read if its running temperature at the time is 60°C​

Answer 1

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If a certain thermometer scale indicates 105.0° and -25.0° has the upper and lower fixed point respectively, what would the scale read if its running temperature at the time is 60°C​

Please Note there is error in your question U.F.P is 105.0°

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This question is slight tricky however let us solve

For conversion of any unit (Temperature) from one unit to another we have a formula

➠    $\dfrac{T- L.F.P }{Number of Divisions} = Constant$   [ T indicates scale type ]

➠ According to this scale We need to calculate it as,

 

GIVEN :

U.F.P = 105.0°

L.F.P =  -25.0°

Total Number of Divisions = ?

T.N.D = U.F.P - L.F.P

         =  105.0° - (-25.0°)

         =  105.0 + 25.0

          = 130

Hence the given scale has 130 total divisions

According to given scale let us substitute in the formula

$\dfrac{T-(-25)}{130} = Constant$  $\longrightarrow equation\: 1$

We need to calculate for 60°C​ so we need to know about Celsius scale

For Celsius scale

$\dfrac{T- L.F.P }{Number of Divisions} = Constant$

$\dfrac{C-0}{100} = Constant$ $\longrightarrow equation\: 2$

[ L.F.P of celsius scale is 0 and no of division is 100]

Equate 1 = 2

$\dfrac{T+25}{130} = \dfrac{C - 0}{100}$

C = 60°C

$\dfrac{T+25}{130} = \dfrac{60 - 0}{100}$

$\dfrac{T+25}{13\cancel 0} = \dfrac{6\cancel 0 }{1\cancel 0\cancel 0}$

T + 25 = 13 × 6

T + 25 = 78

T = 78 - 25

T = 53°C

Hence the given scale would read 53°C if its running temperature at the time is 60°C​

Hope it helps

Thanks for asking :)