Answered

A piston-cylinder device containing a fluid is fitted with a paddle wheel stirring device operated by the fall of an external weight of mass 51kg. As the mass drops by a height of 5.6m, the paddle wheel makes 10100 revolutions. Meanwhile the free moving piston (frictionless and weightless) of 0.51m diameter moves out by a distance of 0.71m. Determine the net work for the system if atmospheric pressure is 101 kPa.

Answer :

Answer:

The value is [tex]W_N = 11849 \ J [/tex]

Explanation:

From the question we are told that

The mass of the external weight is [tex]m = 51 \ kg[/tex]

The height through which the mass drops is [tex]h = 5.6 \ m[/tex]

     The  number of revolution made is   [tex]N  = 10100 \  kg[/tex]

    The  diameter of the free moving piston is     [tex]d  = 0.51 \  m \  kg[/tex]

     The distance moved by the free moving piston is   [tex]s  = 0.71 \  m \  kg[/tex]

     The  atmospheric pressure is  [tex]P  = 101 \ kPa = 101*10^{3}\ Pa [/tex]

Generally the workdone by the  external weight is mathematically represented as

      [tex]W_w  =m *  g   *  h[/tex]

=     [tex]  51 *  9.8  *  5.6 [/tex]

=     [tex]2799 N  [/tex]

Generally the workdone by the free moving piston  is mathematically represented as  

        [tex]W_p  =P *  A  *  s[/tex]

Here   A is the cross-sectional area with value  

        [tex] A  =  \pi *  \frac{d^2}{4}[/tex]

        [tex] A  =  3.142 *  \frac{0.51^2}{4}[/tex]

So

       [tex]W_p  =101*10^{3} * 3.142 *  \frac{0.51^2}{4}  *  0.71[/tex]

=>       [tex]W_p  = 14651 [/tex]

So

   The net workdone is mathematically evaluated as

        [tex]W_N   = -W_w+W_p  [/tex]

The negative sign shows that it is acting in opposite direction to [tex]W_N[/tex]

So

       [tex]W_N   = -2799+14651  [/tex]

      [tex]W_N   = 11849 \ J   [/tex]

Other Questions