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Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits
104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaks
occur in their respective radiation curves is
104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaks
occur in their respective radiation curves is
Correct answer is '2'. Can you explain this answer?
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Two spherical stars A and B emit blackbody radiation. The radius of A ...
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Two spherical stars A and B emit blackbody radiation. The radius of A ...
The ratio of the radii of the two stars is given as 400, which means the radius of A is 400 times that of B.
The ratio of the power emitted by the two stars is given as 104, which means A emits 104 times the power emitted by B.
Let's assume the temperature of star A is T_a and the temperature of star B is T_b.
According to the Stefan-Boltzmann law, the power emitted by a blackbody is proportional to the fourth power of its temperature (P ∝ T^4).
So, we can write the following equation for the power emitted by star A compared to that of star B:
P_a = P_b * (T_a / T_b)^4
Given that P_a / P_b = 104, we can substitute this value into the equation:
104 = (T_a / T_b)^4
Taking the fourth root of both sides, we get:
∛∛∛∛104 = T_a / T_b
41.6 = T_a / T_b
Now, let's consider the ratio of the surface areas of the two stars.
The surface area of a sphere is proportional to the square of its radius (A ∝ r^2).
So, we can write the following equation for the surface area of star A compared to that of star B:
A_a = A_b * (r_a / r_b)^2
Given that r_a / r_b = 400, we can substitute this value into the equation:
A_a = A_b * (400)^2
A_a = A_b * 160,000
Since the power emitted by a blackbody is proportional to its surface area (P ∝ A), we can write:
P_a = P_b * 160,000
Now, we can solve the system of equations:
P_a = P_b * 160,000 (1)
P_a / P_b = 104 (2)
Dividing equation (1) by equation (2), we get:
P_b * 160,000 / P_b = 104
160,000 = 104
This equation is not true, so there must be an error in the given information or in the calculations.
The ratio of the power emitted by the two stars is given as 104, which means A emits 104 times the power emitted by B.
Let's assume the temperature of star A is T_a and the temperature of star B is T_b.
According to the Stefan-Boltzmann law, the power emitted by a blackbody is proportional to the fourth power of its temperature (P ∝ T^4).
So, we can write the following equation for the power emitted by star A compared to that of star B:
P_a = P_b * (T_a / T_b)^4
Given that P_a / P_b = 104, we can substitute this value into the equation:
104 = (T_a / T_b)^4
Taking the fourth root of both sides, we get:
∛∛∛∛104 = T_a / T_b
41.6 = T_a / T_b
Now, let's consider the ratio of the surface areas of the two stars.
The surface area of a sphere is proportional to the square of its radius (A ∝ r^2).
So, we can write the following equation for the surface area of star A compared to that of star B:
A_a = A_b * (r_a / r_b)^2
Given that r_a / r_b = 400, we can substitute this value into the equation:
A_a = A_b * (400)^2
A_a = A_b * 160,000
Since the power emitted by a blackbody is proportional to its surface area (P ∝ A), we can write:
P_a = P_b * 160,000
Now, we can solve the system of equations:
P_a = P_b * 160,000 (1)
P_a / P_b = 104 (2)
Dividing equation (1) by equation (2), we get:
P_b * 160,000 / P_b = 104
160,000 = 104
This equation is not true, so there must be an error in the given information or in the calculations.
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Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaksoccur in their respective radiation curves isCorrect answer is '2'. Can you explain this answer?
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Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaksoccur in their respective radiation curves isCorrect answer is '2'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaksoccur in their respective radiation curves isCorrect answer is '2'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaksoccur in their respective radiation curves isCorrect answer is '2'. Can you explain this answer?.
Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaksoccur in their respective radiation curves isCorrect answer is '2'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaksoccur in their respective radiation curves isCorrect answer is '2'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaksoccur in their respective radiation curves isCorrect answer is '2'. Can you explain this answer?.
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Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaksoccur in their respective radiation curves isCorrect answer is '2'. Can you explain this answer?, a detailed solution for Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaksoccur in their respective radiation curves isCorrect answer is '2'. Can you explain this answer? has been provided alongside types of Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits104 times the power emitted from B. The ratio (λA/λB) of their wavelengths λA and λB at which the peaksoccur in their respective radiation curves isCorrect answer is '2'. Can you explain this answer? theory, EduRev gives you an
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