Question

The freezing point on a thermometer is marked as \[{{20}^{0}}\]and the boiling point as \[{{150}^{0}}\].A temperature of \[{{60}^{0}}C\]on this thermometer will be read as –
\[\begin{align}
  & A){{40}^{0}} \\
 & B){{65}^{0}} \\
 & C){{98}^{0}} \\
 & D){{110}^{0}} \\
\end{align}\]

Answer 1

Hint: For this type of question we have to know the lower values and upper values of temperature scales. When the scale of the thermometer is not known then only degree symbols are used in the unit.
The difference between the lower and upper value of the thermometer gives the number of divisions the scale is divided.

Complete answer:
Temperature is that physical quantity which determines the degree of hotness and coldness of the body. This is measured by a certain thermometer which has different scales for measurement. These different scales of measurement have different unit representations for Celsius Scale \[^{0}C\] is used.
For Fahrenheit scale \[^{0}F\]is used. For Kelvin scale K is used. For the Reaumur Scale \[^{o}R\]is used. Each scale has its Lower Value and Upper Value and the number of divisions on each scale is calculated just by doing the difference between upper value and lower value.
Here it is given in the question that the freezing point on a thermometer is marked = \[{{20}^{0}}\]
and boiling point is market=\[{{150}^{0}}\].
Freezing point is defined as a lower value of temperature on that scale and Boiling point is defined as Upper value of temperature on that scale.
So for this thermometer, the lower value of this thermometer is \[{{20}^{0}}\] and upper value of this thermometer is \[{{150}^{0}}\].
We have to find the temperature of\[{{60}^{0}}C\]in Celsius scale, which is equivalent to the temperature on that thermometer. Let us assume the equivalent temperature on this thermometer is\[{{t}^{o}}C\].
Since we know that for Celsius Scale, Freezing Point is \[{{O}^{0}}C\]and boiling point \[{{100}^{0}}C\]
So, Lower value of Degree Celsius is\[{{O}^{0}}C\]
and the Upper Value of Degree Celsius is\[{{100}^{0}}C\].
Number of division of Celsius scale is calculated as-
\[=100-0\]
\[=100\]
This means that 1 division on the Celsius scale is equivalent to 1 degree Celsius.
We use the formula for temperature conversion is –
\[\dfrac{Temp(Scale)-Lower(Value)}{Upper(Value)-Lower(Value)}\]
\[\Rightarrow \]\[\dfrac{t-20}{150-20}=\dfrac{60-0}{100-0}\]
\[\Rightarrow \]\[\dfrac{t-20}{130}=\dfrac{60}{100}\]
\[\Rightarrow \]\[t-20=\dfrac{60\times 130}{100}\]
\[\Rightarrow \]\[t-20=78\]
\[\therefore \]\[t={{98}^{0}}\]
So the temperature of \[{{60}^{0}}C\]on the Celsius scale is equivalent to the temperature of\[{{98}^{0}}\]on that thermometer.

Option C is Correct.

Note:
For using conversion formula for temperature we have to know the freezing point (lower value) and boiling point (Upper value) of scales. There are four basic scales used to measure temperature.
They are- Celsius Scale; Kelvin scale; Fahrenheit Scale; Reaumur Scale. Reaumur scale is the least used scale for measurement.