Question:
The initial and final temperatures of water as recorded by an observer are $(38.6 \pm 0.2)^\circ\text{C}$ and $(82.3 \pm 0.3)^\circ\text{C}$. The rise in temperature with proper error limits is
The initial and final temperatures of water as recorded by an observer are $(38.6 \pm 0.2)^\circ\text{C}$ and $(82.3 \pm 0.3)^\circ\text{C}$. The rise in temperature with proper error limits is
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Errors always add up, whether you are finding a sum or a difference.
Updated On: May 14, 2026
- $(43.7 \pm 0.2)^\circ\text{C}$
- $(43.7 \pm 0.3)^\circ\text{C}$
- $(43.7 \pm 0.1)^\circ\text{C}$
- $(43.7 \pm 0.5)^\circ\text{C}$
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The Correct Option is D
Solution and Explanation
Step 1: Concept
When two quantities are added or subtracted, the absolute errors are always added.
Step 2: Meaning
Rise in temperature $\Delta T = T_2 - T_1$. $\Delta T = 82.3 - 38.6 = 43.7^\circ\text{C}$.
Step 3: Analysis
Total error $\delta(\Delta T) = \delta T_2 + \delta T_1 = 0.3 + 0.2 = 0.5^\circ\text{C}$.
Step 4: Conclusion
Rise in temperature is $(43.7 \pm 0.5)^\circ\text{C}$. Final Answer: (D)
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