Question

The temperature of a body rises by $1^\circ C$ . What is the corresponding rise on the (a) Fahrenheit Scale (b) Kelvin scale?

Answer 1

Hint:In order to solve this question we need to understand temperature and its measurement scales. Temperature is defined as the quantity which shows how much heated or cooled a body is, to measure the temperature standard international units proposed three scales, Celsius, Kelvin and Fahrenheit out of which Kelvin scale is considered to be standard units for measuring temperature of body. The temperature of the body can be measured in one scale and later by inter conversion formulae we can convert them into another scale.

Complete step by step answer:
We know the relation between Celsius and Fahrenheit as;
$^\circ F = 32 + \dfrac{9}{5}^\circ C \to (i)$
We know, water boils at $100^\circ C$ to find the equivalent temperature in Fahrenheit we use equation (i) as,
${T_1} = 32 + \dfrac{9}{5}(100)$
$\Rightarrow {T_1} = 32 + 180$
$\Rightarrow {T_1} = 212^\circ F$
Also the freezing point of water is $0^\circ C$ to find the equivalent temperature in Fahrenheit we use equation (i) as,
${T_2} = 32 + \dfrac{9}{5}(0)$
$\Rightarrow {T_2} = 32^\circ F$
So units on Celsius scale is defined as difference between boiling and freezing point of water that is,
${U_1} = (100 - 0)^\circ C$
$\Rightarrow {U_1} = 100^\circ C$

Similarly units on Fahrenheit scale is defined as difference between boiling and freezing point of water that is,
${U_2} = {T_1} - {T_2}$
$\Rightarrow {U_2} = (232 - 32)^\circ F$
$\Rightarrow {U_2} = 180^\circ F$
So $100^\circ $ rise on the Celsius scale is equal to $180^\circ $ rise on Fahrenheit scale.
So $1^\circ $ rise in Celsius scale is equivalent to $(\dfrac{{180}}{{100}})^\circ $ rise on Fahrenheit scale. $1^\circ $ rise in Celsius scale is equivalent to $1.8^\circ $ rise on Fahrenheit scale. Similarly Using relation between Kelvin and Celsius as: $K = 273 + ^\circ C$
So freezing point of water in kelvin is,
${T_1}' = 273 + 0^\circ C$
$\Rightarrow {T_1}' = 273K$

And, boiling point of water in kelvin is,
${T_2}' = 273 + 100^\circ C$
$\Rightarrow {T_2}' = 373K$
So units on Celsius scale is defined as difference between boiling and freezing point of water that is,
${U_1} = (100 - 0)^\circ C$
$\Rightarrow {U_1} = 100^\circ C$
So units on Kelvin scale is defined as difference between boiling and freezing point of water that is,
${U_3} = (373 - 273)K$
$\Rightarrow {U_3} = 100K$
So $100^\circ $ rise on the Celsius scale is equal to $100K$ rise on the Kelvin scale.So $1^\circ $ rise in Celsius scale is equivalent to $(\dfrac{{100}}{{100}})K$ rise on Kelvin scale.

Hence, $1^\circ $ rise in Celsius scale is equivalent to $1K$ rise on Kelvin scale.

Note:It should be remembered that out of three scales Kelvin is considered to be standard international unit to measure temperature because kelvin is always positive while Degree Celsius and Degree Fahrenheit both can be negative and thereby creating error in measurement of temperature during various phenomena.