MHT CET · Physics · Thermal Properties of Matter
A' black body radiates power ' \(P\) ' and maximum energy is radiated by it at a wavelength \(\lambda_0\). The temperature of the black body is now so changed that it radiates maximum energy at the wavelength \(\frac{\lambda_0}{4}\). The power radiated by it at new temperature is
- A 64 P
- B 256 P
- C 4 P
- D 16 P
Answer & Solution
Correct Answer
(B) 256 P
Step-by-step Solution
Detailed explanation
According to Wien's displacement law,
\(\lambda_{\text {max }} \mathrm{T}=\) constant
\(\therefore \quad \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{\lambda_{\max _2}}{\lambda_{\max _1}}=\frac{1 / 4 \lambda_0}{\lambda_0}=\frac{1}{4}\)
Power radiated for a blackbody, \(\mathrm{P}=\sigma \mathrm{AT}^4\)
\(\begin{aligned}
\therefore \quad \frac{\mathrm{P}_1}{\mathrm{P}_2} & =\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^4=\left(\frac{1}{4}\right)^4=\frac{1}{256} \\
\mathrm{P}_2 & =256 \mathrm{P}_1=256 \mathrm{P}
\end{aligned}\)
\(\lambda_{\text {max }} \mathrm{T}=\) constant
\(\therefore \quad \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{\lambda_{\max _2}}{\lambda_{\max _1}}=\frac{1 / 4 \lambda_0}{\lambda_0}=\frac{1}{4}\)
Power radiated for a blackbody, \(\mathrm{P}=\sigma \mathrm{AT}^4\)
\(\begin{aligned}
\therefore \quad \frac{\mathrm{P}_1}{\mathrm{P}_2} & =\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^4=\left(\frac{1}{4}\right)^4=\frac{1}{256} \\
\mathrm{P}_2 & =256 \mathrm{P}_1=256 \mathrm{P}
\end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- An alternating voltage \(E=200 \sqrt{2} \sin (100 t)\) volt is connected to a \(1 \mu \mathrm{f}\) capacitor through an a.c. ammeter. The reading of the ammeter shallMHT CET 2023 Easy
- The instantaneous value of current in an a.c. circuit is \(I=3 \sin\) \(\left(50 \pi t+\frac{\pi}{4}\right) \mathrm{A}\). The current will be maximum for the first time atMHT CET 2025 Easy
- When a hydrogen atom is raised from the ground state to the excited stateMHT CET 2024 Easy
- The angle of prism is A and one of its refracting surface is silvered. Light rays falling at an angle of incidence ' \(2 \mathrm{~A}\) ' on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index of the material of the prism isMHT CET 2023 Medium
- When a liquid flows through a tube, the Reynold's number is 900 , the flow of a liquid isMHT CET 2022 Easy
- Two point charges \((A\) and \(B)+4 q\) and \(-4 q\) are placed along a line separated by a distance ' \(r\) '. Force acting between them is F. If \(25 \%\) of charge from point A is transferred to that at
point \(B\), the force between the charges now becomesMHT CET 2024 Easy
More PYQs from MHT CET
- What is value of rate constant of a first order reaction if slope of graph between \(\log _{10} \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_{\mathrm{t}}}\) (y axis) and time (x axis) is \(1 \times 10^{-3}\) ?MHT CET 2022 Easy
- Bulimia is a type of psychosis, which means _____________ .MHT CET 2021 Easy
- Identify the correct decreasing order of atomic radii from following.MHT CET 2022 Easy
- If the line \(\frac{x+1}{2}=\frac{y-m}{3}=\frac{z-4}{6}\) lies in the plane \(3 x-14 y+6 z+49=0\), then the value of \(m\) isMHT CET 2021 Medium
- In the arrangement shown in the figure, the mass ' m ' will ascend with an acceleration (consider pully and rope are massless) ( \(g=\) acceleration due to gravity)
MHT CET 2025 Medium - Copper is a divalent metal. The value of its electrochemical equivalent is \(3.29 \times 10^{-4} \mathrm{~g} .\) Its atomic mass isMHT CET 2009 Medium