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The volume of 1 kg of helium in a piston–cylinder device is initially 5 m3. Now helium is compressed to 2 m3 while its pressure is maintained constant at 130 kPa. Determine the initial and final temperatures of helium as well as the work required to compress it, in kJ. The gas constant of helium is R = 2.0769 kJ/kg·K.

Respuesta :

Answer:

[tex]T_1 = 312.96 K[/tex]

T_2 = 125.18 K

W = -390 kJ

Explanation:

Given data:

Helium mass m = 1 kg

helium intial volume[tex] v_1 = 5 m^3[/tex]

helium final volume [tex]v_2 = 2 m^3[/tex]

Pressure P = 130 kPa

Gas constant R = 2.0769 kJ/kg.K

intial temperature can be computed by using the following formula

[tex]T_1 = \frac{PV_1}{mR}[/tex]

plugging all value  in above equation

[tex]T_1 = \frac{130 \times 5}{1 \times 2.0769}[/tex]

[tex]T_1 = 312.96 K[/tex]

final temperature

[tex]T_2 = \frac{PV_2}{mR}[/tex]

[tex]T_2 = \frac{130 \times 2}{1 \times 2.0769}[/tex]

T_2 = 125.18 K

work  required to compress heilum

[tex]W = P(v_2 - v_1)[/tex]

[tex]W = 130 \times (2 - 5)[/tex]

W = -390 kJ

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