Question

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.

Answer 1

Answer:28.21 kJ/kg

Step-by-step explanation:

Given

`P_1=10\ bar`

`T_1=405\ K`

`T_2=300\ K`

Process
`PV^(1.3)=constant`

Work done for Polytropic process

`W=(P_1V_1-P_2V_2)/(n-1)`

where n=Polytropic index

`W=(R(T_1-T_2))/(n-1)`

`W=(0.296(405-300))/(1.3-1)\quad [R_(N_2)=(8.314)/(28)]`

`W=103.6\ kJ\kg`

Now Calculating change in Internal energy

`\Delta U=c_v(T_2-T_1)`

`\Delta U=0.718* (300-405)`

`\Delta U=-75.39\ kJ/kg`

Now applying First law concept

`\Delta U=Q-W`

`Q=W+\Delta U`

`Q=103.6-75.392`

`Q=28.21\ kJ/kg`