contestada

A gas in a piston-cylinder assembly undergoes a compression process for which the relation between pressure and volume is given by PVn = constant. The initial volume is 0.1 m3 , the final volume is 0.04 m3 , and the final pressure is 2 bar. Determine the initial pressure (bar), and the work for the process, in kJ, if (a) n = 0, (b) n = 1, (c) n = 1.3.

Respuesta :

Explanation:

The given data is as follows.

  [tex]P_{2}[/tex] = 2 bar,     [tex]P_{1}[/tex] = ?

  [tex]V_{1} = 0.1 m^{3}[/tex],    [tex]V_{2} = 0.04 m^{3}[/tex]

We know that,

        [tex]PV^{n}[/tex] = constant

or,     [tex]P_{1}V_{1}^{n} = P_{2}V_{2}^{n}[/tex]

(a)  For n = 0; we will calculate the initial pressure as follows.

       [tex]P_{1}V_{1}^{n} = P_{2}V_{2}^{n}[/tex]

      [tex]P_{1} \times (0.1)^{0} = 2 \times (0.04)^{0}[/tex]

             [tex]P_{1}[/tex] = 2 bar

(b)  For n = 1; we will calculate the initial pressure as follows.

       [tex]P_{1}V_{1}^{n} = P_{2}V_{2}^{n}[/tex]

      [tex]P_{1} \times (0.1)^{1} = 2 \times (0.04)^{1}[/tex]

             [tex]P_{1}[/tex] = 0.8 bar

(c) For n = 1.3; we will calculate the initial pressure as follows.

         [tex]P_{1}V_{1}^{n} = P_{2}V_{2}^{n}[/tex]

      [tex]P_{1} \times (0.1)^{1.3} = 2 \times (0.04)^{1.3}[/tex]

             [tex]P_{1} \times (2.5)^{1.3}[/tex] = 2

            [tex]P_{1}[/tex] = 0.6

Otras preguntas