Question

The temperature of three bodies A, B and C are increased by $1°C,1°F,and1K$, respectively. What will be the relation between these temperatures, if these change in temperature are represented by $∆C,∆Fand∆K$, respectively?

• A. $∆C=∆F=∆K$
• B. $∆C=∆K>∆F$
• C. $∆F>∆C>∆K$
• D. $∆F=∆C>∆K$

Answer 1

The correct option is B

$∆C=∆K>∆F$

Step 1: Given Data:

The temperature of three bodies A, B and C are increased by $1°C,1°F,and1K$, respectively

We have to find relation between the change in temperatures, $∆C,∆Fand∆K$

Step 2: Find the Relation between the $°C,°FandK$

Relation between Celsius and Kelvin Scale

$$\begin{gathered} K=°C+273.15 \\ °C=K-273.15 \end{gathered}$$

Relation between Celsius and Fahrenheit Scale

$$\begin{gathered} °F=\left(\frac{9}{5}\right)\times °C+32 \\ °C=\left(°F-32\right)\times \left(\frac{5}{9}\right) \end{gathered}$$

Relation between all these three scales:

$$\begin{gathered} °C=\left[K-273.15\right]=\left[\left(°F-32\right)\times \left(\frac{5}{9}\right)\right] \\ \frac{°C}{5}=\frac{\left[K-273.15\right]}{5}=\frac{\left[°F-32\right]}{9} \end{gathered}$$

Step 3: Relation between the change in temperatures.

For Initial Temperature, the relation would be:

$\frac{°C_1}{5}=\frac{\left[K_1-273.15\right]}{5}=\frac{\left[°F_1-32\right]}{9}$

For the Final Temperature, the relation would be:

$\frac{°C_2}{5}=\frac{\left[K_2-273.15\right]}{5}=\frac{\left[°F_2-32\right]}{9}$

We will get the change in temperatures by their difference:

$$\begin{gathered} \left(\frac{°C_2}{5}-\frac{°C_1}{5}\right)=\left(\frac{\left(K_2-273.15\right)}{5}-\frac{\left(K_1-273.15\right)}{5}\right)=\left(\frac{°F_2-32}{9}-\frac{°F_1-32}{9}\right) \\ \frac{∆C}{5}=\frac{∆K}{5}=\frac{∆F}{9} \end{gathered}$$

We can clearly see that, $∆C=∆K>∆F$

Hence, option (B) is the correct answer.