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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
Heat Transfer

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Heat Transfer

Consider the situation depicted in the figure. The frame is...

Consider the situation depicted in the figure. The frame is constructed from the same material and possesses a uniform cross-sectional area throughout. Determine the amount of heat flowing per second through a cross section of the bent part, given that the total heat extracted per second from the end at 100^{}^{{}^{\circ}} \text{C} is 130 J130 \text{ J}.
Consider the situation depicted in the figure. The frame is constructed from the same material and possesses a uniform

Options

  1. A70 J70 \text{ J}
  2. B60 J60 \text{ J}
  3. C130 J130 \text{ J}
  4. D65 J65 \text{ J}

Correct answer

B. 60 J60 \text{ J}

Step-by-step solution

The thermal circuit consists of a parallel combination of the straight middle part and the bent part, connected in series with the two end parts.

The length of the straight middle part is L1=60 cmL_1 = 60 \text{ cm}.

The length of the bent part is L2=5 cm+60 cm+5 cm=70 cmL_2 = 5 \text{ cm} + 60 \text{ cm} + 5 \text{ cm} = 70 \text{ cm}.

Since the frame is made of the same material and has a uniform cross-sectional area, the thermal resistance RR of any part is proportional to its length LL (R=LKAR = \dfrac{L}{KA}).

Let the thermal resistance of the straight part be R1=60kR_1 = 60k and that of the bent part be R2=70kR_2 = 70k, where kk is a constant.

The total heat current flowing through the system is given as I=130 J/sI = 130 \text{ J/s}.

In a parallel combination, the heat current divides inversely as the thermal resistance. The heat current I2I_2 flowing through the bent part is:

I2=I×R1R1+R2I_2 = I \times \dfrac{R_1}{R_1 + R_2}

Substituting the values:

I2=130×60k60k+70kI_2 = 130 \times \dfrac{60k}{60k + 70k}

I2=130×60130I_2 = 130 \times \dfrac{60}{130}

I2=60 J/sI_2 = 60 \text{ J/s}
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