Question

Temperature of an object increases by $40$ degrees on the Celsius scale. What are corresponding changes on the Fahrenheit scale and absolute scale?

• A. ${40}^{\circ }\text{F},72\text{K}$
• B. ${72}^{\circ }\text{F},40\text{K}$
• C. ${22.2}^{\circ }\text{F},40\text{K}$
• D. ${40}^{\circ }\text{F},-22.2\text{K}$

Answer 1

The correct option is B ${72}^{\circ }\text{F},40\text{K}$

As $\Delta T={40}^{\circ }\text{C}$, we can choose any 2 temperatures , lets take $0{}^{\circ }\text{C}\&{40}^{\circ }\text{C}$ .

Now, we have to find corresponding $\Delta T_F$ in Fahrenheit scale
$T_{{}^{\circ }\text{C}}=\frac{5}{9}(T_{{}^{\circ }\text{F}}-32)$

Let $T_{F1}$ and $T_{F2}$ be the corresponding temperature on Fahrenheit scale.
Then, $0=\frac{5}{9}(T_{F1}-32)$
$\Rightarrow T_{F1}={32}^{\circ }\text{F}$
Similarly,
$40=\frac{5}{9}(T_{F2}-32)$
$\Rightarrow T_{F2}={104}^{\circ }\text{F}$
$\therefore \Delta T_{{}^{\circ }\text{F}}=104-32={72}^{\circ }\text{F}$

Also, we know $\Delta T_{\circ C}=\Delta T_K$
$\therefore \Delta T_K=40\text{K}$