Question

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.

Answer 1

Explanation:

The given data is as follows.

  $P_{2}$ = 2 bar,     $P_{1}$ = ?

  $V_{1} = 0.1 m^{3}$,    $V_{2} = 0.04 m^{3}$

We know that,

        $PV^{n}$ = constant

or,     $P_{1}V_{1}^{n} = P_{2}V_{2}^{n}$

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

       $P_{1}V_{1}^{n} = P_{2}V_{2}^{n}$

      $P_{1} \times (0.1)^{0} = 2 \times (0.04)^{0}$

             $P_{1}$ = 2 bar

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

       $P_{1}V_{1}^{n} = P_{2}V_{2}^{n}$

      $P_{1} \times (0.1)^{1} = 2 \times (0.04)^{1}$

             $P_{1}$ = 0.8 bar

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

         $P_{1}V_{1}^{n} = P_{2}V_{2}^{n}$

      $P_{1} \times (0.1)^{1.3} = 2 \times (0.04)^{1.3}$

             $P_{1} \times (2.5)^{1.3}$ = 2

            $P_{1}$ = 0.6