SATHEE: Heat and Thermodynamics 3 Question 29

Heat and Thermodynamics 3 Question 29

29. A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated $(P)$ by the metal. The sensor has a scale that displays $\log_{2} (P / P_{0})$ , where $P_{0}$ is a constant. When the metal surface is at a temperature of $487^{\circ} C$ , the sensor shows a value 1 . Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to $2767^{\circ} C$ ?

(2016 Adv.)

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Solution:

$\log_{2} \frac{P_{1}}{P_{0}} = 1$

Therefore, $\frac{P_{1}}{P_{0}} = 2$

According to Stefan’s law,

$\begin{aligned} P & \propto T^{2} \\ \Rightarrow \frac{P_{2}}{P_{1}} & = {(\frac{T_{2}}{T_{1}})}^{4} = {(\frac{2767 + 273}{487 + 273})}^{4} = 4^{4} \\ \Rightarrow \frac{P_{2}}{P_{1}} & = \frac{P_{2}}{2 P_{0}} = 4^{4} \Rightarrow \frac{P_{2}}{P_{0}} = 2 \times 4^{4} \\ \log_{2} \frac{P_{2}}{P_{0}} & = \log_{2} [2 \times 4^{4}] = \log_{2} 2 + \log_{2} 4^{4} \\ = 1 + \log_{2} 2^{8} = 9 \end{aligned}$

Heat and Thermodynamics 3 Question 29

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Heat and Thermodynamics 3 Question 29

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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