A distant star is monitored over several billion years

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A distant star is monitored over several billion years. At the present time (

t_0

) the star’s emitted spectrum reaches its maximum intensity at a wavelength of

\lambda_{\text{peak}}(t_0)=400\,\text{nm}

. Astronomers estimate the current surface temperature of the star to be

T(t_0)=7.2\times10^{3}\,\text{K}

. Observations in the far future (

t_1

) reveal that the peak of the spectrum has shifted to

\lambda_{\text{peak}}(t_1)=700\,\text{nm}

. Assume the star behaves as a blackbody. For the purpose of this problem, neglect any change in the star’s radius between

t_0

and

t_1

. (a) Determine the ratio

T(t_1)/T(t_0)

of the star’s surface temperature at the later time to its current surface temperature. (b) Calculate the surface temperature

T(t_1)

of the star at time

t_1

. (c) Using your result from part (a), compute the ratio of the total power radiated per unit area at

t_1

to that at

t_0

. Clearly state any additional physical laws you use in your reasoning. (d) Despite the temperature change you found, some visible-light observers might still classify the star’s color as "red" at time

t_1

. Provide a qualitative explanation for this classification based on the spectral data given.

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