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Nitrogen (N2) contained in a piston–cylinder arrangement, initially at 10 bar and 405 K, undergoes an expansion to a final temperature of 300 K, during which the pressure–volume relationship is pV1.3 = constant. Assuming the ideal gas model for the N2, determine the heat transfer in kJ/kg.

Respuesta :

Answer:28.21 kJ/kg

Explanation:

Given

[tex] P_1=10\ bar[/tex]

[tex]T_1=405\ K[/tex]

[tex]T_2=300\ K[/tex]

Process [tex]PV^{1.3}=constant[/tex]

Work done for Polytropic process

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

where n=Polytropic index

[tex]W=\dfrac{R(T_1-T_2)}{n-1}[/tex]

[tex]W=\dfrac{0.296(405-300)}{1.3-1}\quad [R_{N_2}=\frac{8.314}{28}][/tex]

[tex]W=103.6\ kJ\kg[/tex]

Now Calculating change in Internal energy

[tex]\Delta U=c_v(T_2-T_1)[/tex]

[tex]\Delta U=0.718\times (300-405)[/tex]

[tex]\Delta U=-75.39\ kJ/kg[/tex]

Now applying First law concept

[tex]\Delta U=Q-W[/tex]

[tex]Q=W+\Delta U[/tex]

[tex]Q=103.6-75.392[/tex]

[tex]Q=28.21\ kJ/kg[/tex]

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