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.

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OlaMacgregor OlaMacgregor · Answer 1 · 2020-03-26T08:18:04+01:00

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