The initial and final temperatures of a water bath are (18 ± 0.5)°C and (40± 0.3)°C. What is the rise in temperature of the bath ?

The correct option is (22 ± 0.8)° C.

Step 1: Calculate the nominal rise in temperature
The initial temperature is given as $T_1=18\text{°C}$ and the final temperature is $T_2=40\text{°C}$.
The rise in temperature, $\mathrm{\Delta T}$, is the difference between the final and initial temperatures:
$\mathrm{\Delta T}=T_2-T_1$
$\mathrm{\Delta T}=40\text{°C}-18\text{°C}=22\text{°C}$

Step 2: Calculate the absolute error in the temperature rise
When two quantities are subtracted (or added), their absolute errors are always added together to find the maximum possible error in the result.
The absolute error in the initial temperature is $\Delta T_1=0.5\text{°C}$.
The absolute error in the final temperature is $\Delta T_2=0.3\text{°C}$.
Therefore, the error in the temperature rise, $\Delta \left(\mathrm{\Delta T}\right)$, is:
$\Delta \left(\mathrm{\Delta T}\right)=\Delta T_1+\Delta T_2$
$\Delta \left(\mathrm{\Delta T}\right)=0.5\text{°C}+0.3\text{°C}=0.8\text{°C}$

Step 3: State the final temperature rise with limits of error
Combining the nominal rise and its error limits, we get:
$\text{Rise in temperature}=(22\pm 0.8)\text{°C}$