- #1

es4

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- Homework Statement
- 0.8 m3 of an experimental gas, compressed from a pressure of, 250 kn/m^2 to pressure of 7000 kn/m^2 . For gas in question, Cp = 1010 & Cv = 732.

Calculate the final volume of each case when gas is compressed.

>>> isothermally

>>> adiabatically

Calculate the final volume when gas is adiabatically compressed & ϒ= 1.5

p1 = 250 or 250000 n/m2

p2 = 7000 or 7000000 n/m2

Cp = 1010

Cv = 732

- Relevant Equations
- p1v1 = p2v2 [Boyle equality law (isothermal process)]

P1 V1^ Y= P2 V2 ^Y [adiabatic Equality law]

Hi, here is my attempt... Feel free to correct me if I am doing it wrong.

v1 = .8 m3

p1 = 250 or 250000 n/m2

p2 = 7000 or 7000000 n/m2

Cp = 1010

Cv = 7321.

p1v1 = p2v2 [Boyle equality law (isothermal process)]

250 000 * .8 = 7000000 * v2

7000000 * v2 = 250 000 * .8

v2 = 250 000 * .8/ 7000 000

v2 = 0285 m3 <<<ans

Y = Cp / Cv

Y = 1010 / 732

y = 1.38

P1 V1^Y= P2 V2^Y [adiabatic Equality law]

250 000 * .8^ 1.38 = 7000000 * v2 ^1.38

7000000 * v2 ^1.38 = 250 000 * .735

7000000 * v2 ^1.38 = 183740.2

v2 ^1.38 = 183740.2/ 7000000

v2 ^1.38 = .0262 <<< what now?

P1 V1^Y= P2 V2^Y [adiabatic Equality law]

250 000 * .8^ 1.5 = 7000000 * v2 ^1.5

7000000 * v2 ^1.5 = 250 000 * .716

7000000 * v2 ^1.38 = 178885.43

v2 ^1.38 = 178885.43/ 7000000

v2 ^1.38 = .0262 <<< what now?

v1 = .8 m3

p1 = 250 or 250000 n/m2

p2 = 7000 or 7000000 n/m2

Cp = 1010

Cv = 7321.

**isothermally**p1v1 = p2v2 [Boyle equality law (isothermal process)]

250 000 * .8 = 7000000 * v2

7000000 * v2 = 250 000 * .8

v2 = 250 000 * .8/ 7000 000

v2 = 0285 m3 <<<ans

**adiabatically**Y = Cp / Cv

Y = 1010 / 732

y = 1.38

P1 V1^Y= P2 V2^Y [adiabatic Equality law]

250 000 * .8^ 1.38 = 7000000 * v2 ^1.38

7000000 * v2 ^1.38 = 250 000 * .735

7000000 * v2 ^1.38 = 183740.2

v2 ^1.38 = 183740.2/ 7000000

v2 ^1.38 = .0262 <<< what now?

### 2. Adiabatic again

y = 1.5 [new value for gamma]P1 V1^Y= P2 V2^Y [adiabatic Equality law]

250 000 * .8^ 1.5 = 7000000 * v2 ^1.5

7000000 * v2 ^1.5 = 250 000 * .716

7000000 * v2 ^1.38 = 178885.43

v2 ^1.38 = 178885.43/ 7000000

v2 ^1.38 = .0262 <<< what now?