Question

The initial and final temperatures of water bath are (18 ± 0.5) °C and (40 ± 0.3) °C
respectively. What is the rise in temperature of bath?
1. (58 ± 0.2) °C
2. (58 ± 0.5) °C
3. (22 ± 0.2) °C
4. (22 ± 0.8) °C

Answer 1

Correct Answer - Option 4 : (22 ± 0.8) °C

Concept:

Error in measurement:

• Sometimes due to inaccuracy in measuring instruments or any other reason, the measured value differs from the true value. 
• The difference in the true value and the measured value of a quantity is called an error of measurement. 
• The true value can be x ± Δx where x is the measured value and Δx is the error. 

Explanation:

Given 

Here, it is given initial temperature of bath = (18 ± 0.5) °C

Final temperature of bath = (40 ± 0.3) °C

So, the minimum initial temperature can be (18 - 0.5 ) °C = 17.5 °C

The maximum initial temperature can be (18 + 0.5 ) °C = 18.5 °C

So, the minimum final temperature can be (18 - 0.5 ) °C = 17.5 °C

The maximum final temperature can be ((40 + 0.3) °C  = 40.3 °C

The minimum final temperature can be ((40 - 0.3) °C  = 39.7 °C

The maximum difference in temperature can be 40.3 °C - 17.5 °C = 22.8 °C

This is the difference between maximum final temperature and minimum initial temperature.

Now, if we will simply subtract the measured values then, the difference in temp will be

S = 40 °C - 18 °C =  22.°C

The maximum difference is 22.8 °C

So, the error could be 22.8 °C - 22.°C = 0.8 °C

So, error will be (22 ± 0.8) °C