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A piston–cylinder device initially contains 0.07 m3 of nitrogen gas at 130 kPa and 180°C. The nitrogen is now expanded to a pressure of 80 kPa polytropically with a polytropic exponent whose value is equal to the specific heat ratio (called isentropic expansion). Determine the final temperature and the boundary work done during this process.

Respuesta :

Answer:

W=2.95 KJ

T₂=394.35 K

Explanation:

Given that

P₁= 130 KPa

V₁=0.07 m³

T₁= 180°C

P₂=80 KPa

Heat capacity ratio for nitrogen gas

γ=1.4

[tex]PV^{\gamma}=C[/tex]

[tex]P_1V_1^{\gamma}=P_2V_2^{\gamma}[/tex]

[tex]V_2=\left(\dfrac{P_1}{P_2}\right)^{\dfrac{1}{\gamma}}V_1[/tex]

[tex]V_2=\left(\dfrac{130}{80}\right)^{\dfrac{1}{1.4}}\times 0.07\ m^3[/tex]

V₂=0.099 m³

[tex]T_2=\left(\dfrac{V_1}{V_2}\right)^{\gamma-1}T_1[/tex]

[tex]T_2=\left(\dfrac{0.07}{0.099}\right)^{1.4-1}\times (273+180)\ K[/tex]

T₂=394.35 K

Work,W

[tex]W=\dfrac{P_1V_1-P_2V_2}{\gamma-1}[/tex]

[tex]W=\dfrac{0.07\times 130-0.099\times 80}{1.4-1}\ KJ[/tex]

W=2.95 KJ  

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