SATHEE: Heat and Thermodynamics 6 Question 1

Heat and Thermodynamics 6 Question 1

5. Consider a spherical shell of radius $R$ at temperature $T$ . The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u = \frac{U}{V} \propto T^{4}$ and pressure $p = \frac{1}{3} (\frac{U}{V})$ . If the shell now undergoes an adiabatic expansion, the relation between $T$ and $R$ is

(2015 Main)

(a) $T \propto e^{- R}$

(b) $T \propto \frac{1}{R}$

(d) $T \propto \frac{1}{R^{3}}$

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Answer:

Correct Answer: 5. (b)

Solution:

Given, $\frac{U}{V} \propto T^{4}$

$\frac{U}{V} = α T^{4}$

It is also given that, $P = \frac{1}{3} (\frac{U}{V})$

$\begin{array}{ll} \Rightarrow & \frac{n R_{0} T}{V} = \frac{1}{3} (α T^{4}) (R_{0} = Gas constant) \\ or & V T^{3} = \frac{3 n R_{0}}{α} = constant \end{array}$

$\begin{aligned} ∴ & (\frac{4}{3} π R^{3}) T^{3} & = constant or R T = constant \\ ∴ & T & \propto \frac{1}{R} \end{aligned}$

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Heat and Thermodynamics 6 Question 1

Answer:

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Heat and Thermodynamics 6 Question 1

5. Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u=UV∝T4 and pressure p=13(UV). If the shell now undergoes an adiabatic expansion, the relation between T and R is

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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