MHT CET · Physics · Thermal Properties of Matter
Three black discs \(x, y, z\) have radii \(1 \mathrm{~m}, 2 \mathrm{~m}\) and \(3 \mathrm{~m}\) respectively. The wavelength corresponding to maximum intensity are \(200 \mathrm{~nm}\), \(300 \mathrm{~nm}\) and \(400 \mathrm{~nm}\) respectively. The relation between emissive power \(E_x, E_y\) and \(E_z\) is
- A \(E_x\) is maximum
- B \(E_y\) is maximum
- C \(E_z\) is maximum
- D \(E_x=E_y=E_z\)
Answer & Solution
Correct Answer
(A) \(E_x\) is maximum
Step-by-step Solution
Detailed explanation
According to the Stefan's Law:
\(\begin{aligned}
& E=\frac{\sigma A T^4}{A} \\
& \Rightarrow E \propto T^4
\end{aligned}\)
According to the Wein's Law:
\(\begin{aligned}
& T=\frac{k}{\lambda_m} \\
& \therefore E \propto \frac{A}{\lambda^4} \\
& E_x: E_y: E_z=\frac{1}{\lambda_x^4}: \frac{1}{\lambda^4}: \frac{1}{\lambda^4}=\frac{1}{200^4}: \frac{1}{300^4}: \frac{1}{400^4}
\end{aligned}\)
The relation between emissive power \(E_x, E_y\) and \(E_z\) is as follows:
\(E x>E y>E z\)
\(\begin{aligned}
& E=\frac{\sigma A T^4}{A} \\
& \Rightarrow E \propto T^4
\end{aligned}\)
According to the Wein's Law:
\(\begin{aligned}
& T=\frac{k}{\lambda_m} \\
& \therefore E \propto \frac{A}{\lambda^4} \\
& E_x: E_y: E_z=\frac{1}{\lambda_x^4}: \frac{1}{\lambda^4}: \frac{1}{\lambda^4}=\frac{1}{200^4}: \frac{1}{300^4}: \frac{1}{400^4}
\end{aligned}\)
The relation between emissive power \(E_x, E_y\) and \(E_z\) is as follows:
\(E x>E y>E z\)
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
- In LCR series resonance circuit, choose the wrong statement.MHT CET 2022 Medium
- The temperature of a gas is \(-80^{\circ} \mathrm{C}\). To what temperature the gas should be heated so that the r.m.s. speed is increased by 2 times?MHT CET 2024 Medium
- An air filled parallel plate capacitor has a uniform electric field 'E' in the space between the plates. If the distance between the plates is 'd' and area of each plate is ' \(A^{\prime}\), the energy stored in the capacitor is \(\left(\epsilon_{0}=\right.\) permittivity of free space)MHT CET 2020 Medium
- A sample of oxygen gas and a sample of hydrogen gas both have the same mass, same volume and the same pressure. The ratio of their absolute temperature is (Molecular wt. of \(\mathrm{O}_2 \& \mathrm{H}_2\) is 32 and 2 respectively)MHT CET 2024 Easy
- In the second orbit of hydrogen atom, the energy of an electron is ' \(E\) '. In the third orbit of helium atom, the energy of the electron will be (atomic number of helium \(=2\) )MHT CET 2024 Easy
- The difference in the acceleration due to gravity at the pole and equator is ( \(g=\) acceleration due to gravity, \(R=\) radius of earth, \(\theta=\) latitude, \(\omega=\) angular velocity, \(\cos 0^{\circ}=1, \cos 90^{\circ}=0\) )MHT CET 2022 Medium
More PYQs from MHT CET
- A body is moving along the horizontal surface with a velocity of \(4 \mathrm{~m} / \mathrm{s}\). If the coefficient of kinetic friction is \(0.2\), the distance travelled by body before coming to rest is \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)\)MHT CET 2020 Easy
- The numbers can be formed using the digit \(1,2,3,4,3,2,1\) so that odd digits always occupy odd places in
ways.MHT CET 2021 Medium - If \(4 \sin ^{-1} x+\cos ^{-1} x=\pi\) then \(x=\)MHT CET 2025 Easy
- In reverse bias \(p n\) -junction diode depletion layer widthMHT CET 2011 Easy
- The area of the square increases at the rate of \(0.5 \mathrm{~cm}^{2} / \mathrm{sec}\). The rate at which its
perimeter is increasing when the side of the square is \(10 \mathrm{~cm}\) long, isMHT CET 2020 Easy - The co-ordinates of the points on the line \(2 x-y=5\) which are the distance of 1 unit from the line \(3 x+4 y=5\) areMHT CET 2023 Medium