Agas 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, in bar, and the work for the process, in kj, if (a) n = 0, (b) n = 1, (c) n = 1.3

A)P1=2 [bar] , W=-12 [kJ]

B)P1=0.8 [bar] , W=-7.3303 [kJ]

C)P1=0.6077 [bar] , W=-6.4091 [kJ]

Explanation:

First, from the problem we know the following information:

V1=0.1 m^3

V2=0.04 m^3

P2=2 bar =200 kPa

The relation PV^n=constant means PV^n is a constant through all the process, so we can derive the initial pressure as:

a) To the case a) the constant n is equal to 0, we can calculate the initial pressure substituting n=0 in the previous expression, so:

The expression to calculate the work is:

If n=0:

Then:

The work is:

b) To the case b) the constant n is equal to 1, we can calculate the initial pressure substituting n=1 in the initial expression, so:

If n=1 then:

To calculate the work:

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Substituting:

c) To the case c) the constant n is equal to 1.3, we can calculate the initial pressure substituting n=1.3 in the initial expression, so:

First:

The work:

Substituting:

W=-6.4091 kJ

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