Question

The coefficient of linear expansion of copper is 17 × 10-6 K-1. A block of copper 30 cm wide, 45 cm long, and 10 cm thick is heated from 0°C to 100°C What is the change in the volume of the block?

Answers

  1. Answer:

    The change in volume is  \Delta V = 0.0001 \ m^3    

    Explanation:

    From the question we are told that

       The coefficient of linear expansion is  \alpha = 17 *10^{-6} \ K^{-1}

       The width  of the block is  b = 30 \ cm = 0.3 \ m

        The length is  l = 45 \ cm = 0.45 \ m

            The thickness is  h = 10 \ cm = 0.1 \ m

         The initial temperature is  T_1 = 0^oC

        The final temperature is  T_f = 100 ^oC

    The  initial volume is  mathematically represented as

            V = l*b*h

    substituting values

         V = 0.30 * 0.45 * 0.10

         V = 0.0135 \ m^3

    Generally the expansion equation is mathematically represented as

             l' = l (1 + \alpha \Delta T)

    where  l' is the new length

    substituting values

            l' = 0.45 (1 + 17*10^{-6} * (100-0))

          l' = 0.4508 \ m

    The new width is evaluated as

         b' = b(1 + \alpha \Delta T )

    substituting values

        b'=0.30 ( 1 + 17*10^{-6} * (100 - 0))

       b'= 0.3005 \ m

    The new thickness is  

        h' = h(1 + \alpha \Delta T )

    substituting values

        h' = 0.10 (1 + (17*10^{-6}) (100 - 0) )

       h' = 0.1001 \ m

    The new volume is  mathematically evaluated as

        V' = l'*b'* h'

    substituting values

       V' = 0.4508 * 0.3005 * 0.1001

        V' = 0.0136

     Therefore

            \Delta V = 0.0136 - 0.0135    

            \Delta V = 0.0001 \ m^3    

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