Question

If a thermometer reads the freezing point of water as 20 degrees Celsius and boiling point as 150 degrees. Celsius, how much kilometers read when the actual temperature is 60 degree Celsius.
A). 98 degree Celsius
B). 110 degree Celsius
C). 150 degree Celsius
D). 60 degree Celsius

Answer 1

Here’s the expression. With the help of scale we calculate the temperature
$\dfrac{{t - freezing{\text{ temp}}}}{{boiling{\text{ temp - freezing temp}}}} = \dfrac{{actual\; temperature}}{{100}}$

Complete step by step solution:
Given,
Freezing temperature is equal to 20 degree Celsius
Boiling temperature is equal to 150 degree Celsius
Actual temperature is equal to 60 degree Celsius
We, measure it by a scale
Here’s the expression to solving the new reading of the thermometer
$\dfrac{c}{{100}} = \dfrac{{t - {t_f}}}{{{t_b} - {t_f}}}$ --- (A)
Here’s
C is the actual temperature,
t is the reading of new thermometer,
$t_b$ is the boiling temperature,
$t_f$ is the freezing temperature
we know the values of
actual temperature that is 60 degree Celsius,
boiling temperature that is 20 degree Celsius,
freezing temperature that is 150 degree Celsius
Put the value in equation(A)
$\dfrac{{60}}{{100}} = \dfrac{{t - 20}}{{150 - 20}}$
Now, we solve for the reading of new thermometer
$\dfrac{{60}}{{100}} = \dfrac{{t - 20}}{{150 - 20}} \\\ \Rightarrow \dfrac{6}{{10}} = \dfrac{{t - 20}}{{130}} \\\$
Now, we do cross multiply
$130 \times 6 = 10(t - 20) \\\ \Rightarrow 780 = 10t - 200 \\\$
Now, separate them one side be variable and other side be the numeric term
$780 + 200 = 10t \\\ \Rightarrow 980 = 10t \\\ \Rightarrow t = \dfrac{{980}}{{10}} \\\ \Rightarrow t = {98^0} \\\$
Here, we get the value of the reading of the new thermometer with the help of boiling point, freezing point and actual temperature.
Now, the temperature is 98 degree Celsius
So, the option (A) is correct.

Note: The thermometer is the instrument for measuring the temperature of a system. In the thermodynamics there is an important role of the thermometer to calculate the change in temperature. In simple terms, if we have to calculate the change in temperature then we have to subtract the old temperature from the new one.