A heat conducting rod, 0.90 m long, is made of an aluminum section, 0.20 m long, and a copper section, 0.70 m long. Both sections have a cro

Question

A heat conducting rod, 0.90 m long, is made of an aluminum section, 0.20 m long, and a copper section, 0.70 m long. Both sections have a cross-sectional area of 0.0004 m^2. The aluminum end and the copper end are maintained at temperatures of 30*C and 230*C respectively. The thermal conductivities of aluminum and copper are 205 and 385 W/m ? K, respectively. The temperature of the aluminum-copper junction in the rod, in *C, is closest to:

in progress 0
Hồng Cúc 6 months 2021-07-14T06:54:04+00:00 1 Answers 34 views 0

Answers ( )

    0
    2021-07-14T06:56:02+00:00

    Answer:

    is closest to  100*C  temperature  at the aluminum-copper junction

    Explanation:

    The expression for calculating the resistance of each rod is given by

    R =\frac{ L}{ kA}

    Now; for Aluminium

    R_{al} =\frac{ 0.20 }{ 205*0.0004}

    R_{al} = 2.439

    For Copper

    R_{Cu}=\frac{0.70}{385*0.0004}

    R_{Cu} = 4.545

    Total Resistance R = R_{al} + R_{Cu}

    = 2.439 + 4.545

    = 6.9845

    Total temperature  difference = 230*C + 30*C

    = 200 *C

    The Total rate of heat flow is then determined which is  = \frac{ total \ temp \ difference}{total \ resistance }

    =\frac{200}{  6.9845 }

    = 28.635 Watts

    However. the temperature difference across the aluminium = Heat flow × Resistance of aluminium

    = 28.635 × 2.349

    = 69.84 *C

    Finally. for as much as one end of the aluminium is = 30 *C , the other end is;

    =30*C + 69.84*C  

    = 99.84  *C

    which is closest to  100*C  temperature  at the aluminum-copper junction

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )