JEE Main 2015PhysicsThermodynamicsHardMCQ

JEE Main 2015 — Thermodynamics Question with Solution

JEE Main 2015 (04 Apr)

Question

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=13UV . If the shell now undergoes an adiabatic expansion the relation between T and R is:

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Show full solutionCorrect option: D
Correct answer
DT∝1R

Step-by-step explanation

∵  in an adiabatic process.

Q=0

So by first law of thermodynamics

Q=dU+W

⇒0=dU+W

⇒W=-dU

∴W=PdV

⇒PdV=-dU ....(i)

Given that UV∝T4⇒U=kVT4

⇒dU=kdVT4=KT4dV+4T3V dT

Also, P=13UV=13kVT4V=KT43 

Putting these values in equation (i)

⇒KT43dV=-kT4dV+4T3V dT

⇒TdV3=-TdV-4VdT

⇒4T3dV=-4VdT

⇒13dVV=-dTT

⇒13ln⁡V=-ln⁡T ⇒ln⁡V=ln⁡T-3

⇒VT3=constant

43πR3 T3=constant

RT=constant

⇒T∝1R

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About this question

This is a previous-year question from JEE Main 2015, covering the Thermodynamics chapter of Physics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.