The following experimental observations were recorded for three separate blackbody…

PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

The following experimental observations were recorded for three separate blackbody sources: λmax=480 nm,T=6000 Kλmax=970 nm,T=3000 Kλmax=2900 nm,  T=1000 K\begin{aligned} \lambda_{\text{max}} &= 480\,\text{nm}, \qquad T = 6000\,\text{K} \\ \lambda_{\text{max}} &= 970\,\text{nm}, \qquad T = 3000\,\text{K} \\ \lambda_{\text{max}} &= 2900\,\text{nm}, \; T = 1000\,\text{K} \end{aligned} Taking each pair of data in turn: (i) Compute the product λmaxT\lambda_{\text{max}}T for all three sources, expressing the result in \text{m\,K}. (ii) Comment on the constancy (or otherwise) of the product obtained and hence state whether the experimental evidence supports the theoretical relation between λmax\lambda_{\text{max}} and TT. (iii) Taking the average of the three values, determine an experimental value of the constant involved in the relation, giving your answer to three significant figures in SI units. (iv) The accepted value of this constant is 2.898×10−3 m K2.898\times10^{-3}\,\text{m\,K}. Calculate the percentage error in the experimentally obtained value.

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