MHTCET 18 Apr 2026 Shift 2 Paper

Concept:Wien's displacement law relates the wavelength of maximum emission to temperature, and Stefan's law relates emissive power to the fourth power of temperature.Explanation:For a black body, Wien's displacement law gives:$$\lambda_{m} T = \text{constant}$$Initially, the maximum energy is at wavelength $\lambda$ and temperature $T_1$.Thus, $\lambda T_1 = \text{constant}$.When the temperature changes to $T_2$, the wavelength becomes $\frac{2\lambda}{3}$.Applying Wien's law again:$$\frac{2\lambda}{3} \times T_2 = \lambda T_1$$Cancelling $\lambda$ from both sides:$$\frac{2}{3} T_2 = T_1$$Therefore,$$T_2 = \frac{3}{2} T_1$$According to Stefan's law, emissive power $E$ is proportional to $T^4$:$$E \propto T^4$$So the ratio of new emissive power $E_2$ to the original emissive power $E$ is:$$\frac{E_2}{E} = \left(\frac{T_2}{T_1}\right)^4$$Substitute $T_2 = \frac{3}{2} T_1$:$$\frac{E_2}{E} = \left(\frac{3}{2}\right)^4 = \frac{81}{16}$$Hence, the new emissive power is $\frac{81}{16}E$.Answer:The emissive power becomes $\frac{81}{16}E$.Correct option: B. $\frac{81}{16}E$