 Solution

ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/section-a/6/solution

For background-subtracted radiative temperature uncertainty, assume the two quoted precisions are independent standard uncertainties, and treat the radiative proportionality factor as known. Write

P_{B} = B

and

P_{T} = 10 B

. Then

P_{S} = 9 B

, while both absolute input uncertainties equal

0.5 B

. Consequently

σ_{S} = (0.05 \times 10 B)^{2} + (0.50 B)^{2} = \frac{B}{2}, \frac{σ _{T}}{T} = \frac{1}{4} \frac{σ _{S}}{P _{S}} .

Thus the temperature precision is about $1.96%$ , or $2%$ . Subtraction amplifies fractional uncertainty even though

P_{T}

itself is precise.

Independence is a measurement assumption, not a consequence of the two percentages. For correlation coefficient

r_{c}

, the result is

σ_{T} / T = 2 (1 - r_{c}) /72

. If the percentages are strict error bounds combined pessimistically, the corresponding bound is

2.78%

. Unknown calibration correlations cannot be inferred from the source.

 New to topics? Read the docs here!