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AP EAMCET201923 Apr 2019Morning ShiftPhysicsThermal Properties of MatterActual

Three rods each of length (l ) and cross sectional area (A ) joined in series between two heat reservoirs as shown in the figure. Their conductivities are (2 K, K ) and ( K 2 ), respectively. Assuming that the conductors are insulated from surroundings, the temperatures (T₁ ) and (T₂ ) of the junctions in steady state condition are respectively.

Options

  1. A( 600 7 ^ C , 400 7 ^ C )
  2. B( 600 7 ^ C , 700 4 ^ C )
  3. C( 500 6 ^ C , 600 5 ^ C )
  4. D( 600 4 ^ C , 400 7 ^ C )

Correct answer

A. ( 600 7 ^ C , 400 7 ^ C )

Step-by-step solution

Key idea In a series combination of heat conductors, the rate of heat flow remains constant. According to the question, the figure given below shows the conduction of heat through series combinations of rods. where, (T₁, T₂= ) temperature of junctions, (I= heat current = d Q d t ) As, ( d Q₁ d t = d Q₂ d t = d Q₃ d t = T_i-T_f k_ eq ) So, ( k₁ A₁ (T_i-T₁ ) l₁ = k₂ A₂ (T₁-T₂ ) l₂ = k₃ A₃ (T₂-T_f ) l₃ ) ( array rlrl & & A₁ & =A₂=A₃ & and & l₁ & =l₂=l₃ & 2 k (100-T₁ ) & =k (T₁-T₂ )=0.5 (T₂-0 ) (i) array ) Equivalent c

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