A cylindrical rod of length 64 cm and cross-section radius r=(2/π) cm is placed at a distance 50 r from a infrared point source S of power 1.25 kW as shown in the figure. The lateral surface of the rod is perfectly insulated from the surroundings. The cross-section A absorbs 80% of the incident energy, has temperature TA in steady state. The surface B is radiating energy into space and the wavelength emitted by it with maximum energy density is 100,000A∘. Find the value of TA (temperature of end A in Kelvin) if conductivity varies with temp as K=TTA. Assume that the rate of flow of heat through the rod is steady.(Wein’s constant = 0.003mK)

Question

A cylindrical rod of length 64 cm and cross-section radius r=(2/π) cm is placed at a distance 50 r from a infrared point source S of power 1.25 kW as shown in the figure. The lateral surface of the rod is perfectly insulated from the surroundings. The cross-section A absorbs 80% of the incident energy, has temperature TA in steady state. The surface B is radiating energy into space and the wavelength emitted by it with maximum energy density is 100,000A∘. Find the value of TA (temperature of end A in Kelvin) if conductivity varies with temp as K=TTA. Assume that the rate of flow of heat through the rod is steady.(Wein’s constant = 0.003mK)

Infinity Learn · Accepted Answer

Intensity of the source at the cross-section ⇒l=P4π(50r)2=1.25×1034π(50r)2Power absorbed by the end ATB=0.003100000×10−10=300K ∫0L0.1TA.dx4×10−4=−∫TATBTdT⇒TA=500K

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