Question 341:
moderateThree stars A, B, C have surface temperatures $T_A$, $T_B$, $T_C$ respectively. Star A appears bluish, star B appears reddish and star C yellowish. Hence, (2020-Covid)
According to Wien's displacement law, $\lambda_{max} \propto \frac{1}{T}$. The wavelength of red is greater than yellow, which is greater than blue ($\lambda_B > \lambda_C > \lambda_A$). Therefore, the temperatures will be in the reverse order: $T_A > T_C > T_B$.
Question 342:
moderateThe power radiated by a black body is $P$ and it radiates maximum energy at wavelength, $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4}\lambda_0$, the power radiated by it becomes $nP$. The value of $n$ is: (2018)
From Wien's displacement law, $T \propto 1/\lambda_{max}$. Thus $T'/T = \lambda_0 / (3\lambda_0/4) = 4/3$. According to Stefan's law, Power $P \propto T^4$. So, $P'/P = (T'/T)^4 = (4/3)^4 = 256/81$.
Question 343:
moderateA spherical black body with a radius of $12\text{ cm}$ radiates $450\text{ watt}$ power at $500\text{ K}$. If the radius were halved and the temperature doubled, the power radiated in watt would be: (2017-Delhi)
Power radiated $P = \sigma A T^4 = \sigma (4\pi r^2) T^4 \Rightarrow P \propto r^2 T^4$. Given $r' = r/2$ and $T' = 2T$. Thus, $P' = P(1/2)^2 (2)^4 = P(1/4)(16) = 4P = 4 \times 450 = 1800\text{ W}$.
Question 344:
moderateA black body is at a temperature of $5760\text{ K}$. The energy of radiation emitted by the body at wavelength $250\text{ nm}$ is $U_1$, at wavelength $500\text{ nm}$ is $U_2$ and that at $1000\text{ nm}$ is $U_3$. Wien’s constant, $b = 2.88 \times 10^6\text{ nmK}$. Which of the following is correct? (2016 – I)
From Wien's displacement law, $\lambda_{max} = \frac{b}{T} = \frac{2.88 \times 10^6}{5760} = 500\text{ nm}$. This means maximum energy is radiated at $500\text{ nm}$. Therefore, the energy $U_2$ is maximum, so $U_2 > U_1$ and $U_2 > U_3$.
Question 345:
moderateOn observing light from three different stars P, Q and R, it was found that intensity of violet color is maximum in the spectrum of P, the intensity of green color is maximum in the spectrum of R and the intensity of red color is maximum in the spectrum of Q. If $T_P$, $T_Q$ and $T_R$ are the respective absolute temperatures of P, Q and R then it can be concluded from the above observations that: (2015)
The wavelengths corresponding to maximum intensity are $\lambda_P < \lambda_R < \lambda_Q$ because violet has the shortest wavelength and red has the longest. From Wien's law, $T \propto 1/\lambda_{max}$. Thus, the temperatures are in the reverse order: $T_P > T_R > T_Q$.
Question 346:
moderateA piece of iron is heated in a flame. It first becomes dull red then becomes reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using: (2013)
As the temperature of the iron increases, the wavelength at which it emits maximum energy decreases, according to Wien's displacement law ($lambda_{max} T = text{constant}$). This causes the color to shift from longer wavelengths (red) to shorter wavelengths (yellow, then all visible mixing to white).
Question 347:
moderateA block body at $1227^{\circ}\text{C}$ emits radiations with maximum intensity at a wavelength of $5000\text{ \AA}$. If the temperature of the body is increased by $1000^{\circ}\text{C}$, the maximum intensity will be observed at (2006)
From Wien's displacement law, $\lambda_m T = \text{constant}$. $\lambda_1 T_1 = \lambda_2 T_2 \Rightarrow 5000 \times (1227+273) = \lambda_2 \times (1227+1000+273) \Rightarrow \lambda_2 = \frac{5000 \times 1500}{2500} = 3000\text{ \AA}$.
Question 348:
moderateWe consider the radiation emitted by the human, body. Which of the following statements is true: (2003)
The temperature of the human body is about $310 \text{ K}$. According to Wien's law, the maximum emission wavelength is around $9.3 \mu\text{m}$, which falls in the infrared region.
Question 349:
moderateThe Wien’s displacement law express relation between (2002)
Wien's displacement law states that the wavelength $\lambda_m$ corresponding to maximum spectral emissive power of a black body is inversely proportional to its absolute temperature $T$. So, it relates $\lambda_m$ and $T$.
Question 350:
moderateWhich of the following is best close to an ideal black body: (2002)
Ferry's black body consists of a hollow double-walled sphere with a small opening. Radiation entering it suffers multiple reflections and gets absorbed. So a cavity maintained at constant temperature is the closest to an ideal black body.