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The temperatures of two bodies measured by a thermometer are t1 = 20 °C ± 0.5 °C and t2 = 50 °C ± 0.5 °C. The temperature difference and the error there is
- a)30 °C ± 1 °C
- b)70 °C ± 0.5 °C
- c)30 °C ± 0.5 °C
- d)70 °C ± 1 °C
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The temperatures of two bodies measured by a thermometer are t1= 20 &d...
Here, t1 = 20 °C ± 0.5 °C; t2 = 50 °C ± 0.5 °C
The temperature difference of two bodies is
t = t2 - t1 = 50 °C - 20 °C = 30 °C
The error in temperature difference is given by
Δt = (Δt1, + Δt2) = (0.5 °C + 0.5 °C) = 1 °C
∴ The temperature difference is 30 °C ± 1 °C.
The temperature difference of two bodies is
t = t2 - t1 = 50 °C - 20 °C = 30 °C
The error in temperature difference is given by
Δt = (Δt1, + Δt2) = (0.5 °C + 0.5 °C) = 1 °C
∴ The temperature difference is 30 °C ± 1 °C.
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Community Answer
The temperatures of two bodies measured by a thermometer are t1= 20 &d...
Understanding Temperature Difference
To find the temperature difference between two bodies, we subtract the two temperature readings:
- t1 = 20 °C ± 0.5 °C
- t2 = 50 °C ± 0.5 °C
Calculating the Difference
The difference in temperature (ΔT) is calculated as follows:
- ΔT = t2 - t1 = 50 °C - 20 °C = 30 °C
Calculating the Error in Temperature Difference
To find the total error in the temperature difference, we consider the errors associated with each measurement. The rule for adding errors states that when subtracting two measurements, the errors add up:
- Error in t1 = 0.5 °C
- Error in t2 = 0.5 °C
Thus, the total error in ΔT is:
- Total Error = Error in t1 + Error in t2 = 0.5 °C + 0.5 °C = 1 °C
Final Result
Combining the calculated temperature difference and the total error, we arrive at:
- ΔT = 30 °C ± 1 °C
Conclusion
The correct answer is a) 30 °C ± 1 °C as it accurately represents the temperature difference and its associated error based on the measurements provided. Other options do not correctly reflect this calculation.
To find the temperature difference between two bodies, we subtract the two temperature readings:
- t1 = 20 °C ± 0.5 °C
- t2 = 50 °C ± 0.5 °C
Calculating the Difference
The difference in temperature (ΔT) is calculated as follows:
- ΔT = t2 - t1 = 50 °C - 20 °C = 30 °C
Calculating the Error in Temperature Difference
To find the total error in the temperature difference, we consider the errors associated with each measurement. The rule for adding errors states that when subtracting two measurements, the errors add up:
- Error in t1 = 0.5 °C
- Error in t2 = 0.5 °C
Thus, the total error in ΔT is:
- Total Error = Error in t1 + Error in t2 = 0.5 °C + 0.5 °C = 1 °C
Final Result
Combining the calculated temperature difference and the total error, we arrive at:
- ΔT = 30 °C ± 1 °C
Conclusion
The correct answer is a) 30 °C ± 1 °C as it accurately represents the temperature difference and its associated error based on the measurements provided. Other options do not correctly reflect this calculation.
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