Railways Technical Ability Vibration Analysis Question Bank Vibration Analysis

  • question_answer The earth receives at its surface radiation from the sun at the rate of \[1400\,\,\text{W/}{{\text{m}}^{\text{2}}}.\] the distance of centre of sun from the surface of earth is \[1.5\times {{10}^{11}}m\] and the radius of sun is \[7.0\times {{10}^{8}}M.\] what is approximately the surface temperature of the sun treating the sun as a black body?

    A) 3650 K             

    B) 4500 K

    C) 5800 K             

    D) 6150 K

    Correct Answer: C

    Solution :

    Temperature of the Sun, \[{{T}_{s}}={{\left[ \frac{{{L}^{2}}{{G}_{s}}}{{{r}^{2}}\sigma } \right]}^{1/4}}\] Where L = mean distance between the sun and the Earth \[=1.5\times {{10}^{11}}m\] r = radius of the Sun \[=7\times {{10}^{8}}m\] \[{{G}_{s}}=\] rate of radiation from the sun \[=1400\,\text{W/}{{\text{m}}^{\text{2}}}\] \[\sigma \,\,=\] Stefan-Boltzmann constan \[=5.675\times {{10}^{-\,8}}\,\text{W/(}{{\text{m}}^{\text{2}}}\text{.K)}\] \[{{T}_{s}}={{\left[ \frac{{{(1.5\times {{10}^{11}})}^{2}}\times 1400}{{{(7\times {{10}^{8}})}^{2}}\times 5.675\times {{10}^{-\,8}}} \right]}^{1/4}}\] = 5800 K \[=900w/{{m}_{2}}\]


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