Physics, 23.03.2020 22:34 Jasten

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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Answer from: seiglersteven99

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

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

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

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

$P_{1}$ = 0.6

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