MHT CET · Physics · Thermal Properties of Matter
A sphere is at temperature 600 K . In an external environment of 200 K , its cooling rate is ' \(R\) '. When the temperature of the sphere falls to 400 K , then cooling rate ' \(R\) ' will become
- A \(\frac{3}{16} \mathrm{R}\)
- B \(\frac{9}{16} R\)
- C \(\frac{16}{9} \mathrm{R}\)
- D \(\frac{16}{3} \mathrm{R}\)
Answer & Solution
Correct Answer
(A) \(\frac{3}{16} \mathrm{R}\)
Step-by-step Solution
Detailed explanation
The rate energy emission from a hot surface is given by Stefan-Boltzmann Law.
\(\therefore \quad \mathrm{R}=\mathrm{e} \mathrm{\sigma A}\left(\mathrm{~T}^4-\mathrm{T}_0^4\right)\)
Hence, \(\frac{\mathrm{R}^{\prime}}{\mathrm{R}}=\frac{\left(400^4-200^4\right)}{\left(600^4-200^4\right)}=\frac{(256-16) \times 10^8}{(1296-16) \times 10^8}=\frac{3}{16}\)
\(\therefore \quad \mathrm{R}^{\prime}=\frac{3}{16} \mathrm{R}\)
\(\therefore \quad \mathrm{R}=\mathrm{e} \mathrm{\sigma A}\left(\mathrm{~T}^4-\mathrm{T}_0^4\right)\)
Hence, \(\frac{\mathrm{R}^{\prime}}{\mathrm{R}}=\frac{\left(400^4-200^4\right)}{\left(600^4-200^4\right)}=\frac{(256-16) \times 10^8}{(1296-16) \times 10^8}=\frac{3}{16}\)
\(\therefore \quad \mathrm{R}^{\prime}=\frac{3}{16} \mathrm{R}\)
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
- A single slit diffraction pattern is formed with white light. For what wavelength of light the \(4^{\text {th }}\) secondary maximum in diffraction pattern coincides with the \(3^{\text {rd }}\) secondary maximum in the pattern of light of wavelength ' \(\lambda\) ' ?MHT CET 2025 Medium
- An inductor of \(0.5 \mathrm{mH}\), a capacitor of \(20 \mu \mathrm{F}\) and a resistance of \(20 \Omega\) are connected in series with a \(220 \mathrm{~V}\) a.c. source. If the current is in phase with the e.m.f. the maximum current in the circuit is \(\sqrt{x} A\). The value of ' \(x\) ' isMHT CET 2023 Hard
- Two galvanometers ' \(A\) ' and 'B' require currents of \(4 \mathrm{~mA}\) and \(7 \mathrm{~mA}\), respectively to produce the same deflection of 20 divisions. If ' \(\mathrm{S}_{A}{ }^{\prime}\) and \({ }^{\prime} \mathrm{S} \mathrm{B}^{\prime}\) are their sensitivities,
respectively, thenMHT CET 2020 Easy - End correction at open end for air column in a pipe of length ' \(l\) ' is ' \(e\) '. For its second overtone of an opern pipe, the wavelength of the wave isMHT CET 2023 Medium
- Two identical blocks each of mass ' \(M\) ' attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. A small mass ' \(m\) ' is now placed on the block B. The acceleration with which the two blocks move together is
[ \(\mathrm{g}=\) gravitational acceleration]
MHT CET 2024 Medium - Due to surface tension, the excess pressure inside a smaller drop is 9 units. If 27 smaller drops combine, then the excess pressure inside the bigger drop isMHT CET 2020 Easy
More PYQs from MHT CET
- \(\bar{a}=\hat{i}+\hat{j}+\hat{k}, \bar{b}=4 \hat{i}-2 \hat{j}+3 \hat{k}, \bar{c}=\hat{i}-2 \hat{j}+\hat{k}\), then \(a\) vector of magnitude 6 units, which is parallel to the vector \(2 \bar{a}-\bar{b}+3 c\), isMHT CET 2024 Easy
- The approximate value of \((3.978)^{\frac{3}{2}}\) isMHT CET 2024 Easy
- Consider two SHMs along the same straight line \(x_1=A_1 \sin \left(\omega t+\phi_1\right)\), \(x_2=A_2 \sin \left(\omega t+\phi_2\right)\), where \(A_1\) and \(A_2\) are their amplitudes and \(\phi_1\) and \(\phi_2\) are their initial phase angle. If the two SHMs meet simultaneously and \(R\) is the resultant amplitude, match column I with column II.MHT CET 2022 Hard
- Which among the following amino acids NOT synthesized in our body?MHT CET 2022 Easy
- Which from following cations in their respective oxidation states develops colourless aqueous solution?MHT CET 2023 Easy
- A particle is executing a linear simple harmonic motion. Let ' \(\mathrm{V}_1\) ' and ' \(\mathrm{V}_2\) ' are its speed at distance ' \(x_1\) ' and ' \(x_2\) ' from the equilibrium position. The amplitude of oscillation isMHT CET 2024 Hard