Question

Air with c_v = 0.723 KJ/Kg_m - °R is compressed in a piston-cylinder machine according to pV^1.3 = c from an initial temperature of 17°C and pressure of 1 bar, to a final pressure of 5 bars. Determine the final temperature, the heat transferred and the work.

Answer 1

c_v = 0.723 KJ/Kg_m - °R,pV^1.3 = c,$T_1$ =17°C and pressure of P₁=1 bar, to a final pressure of ,P₂=5 bars.

As per polytropic relation

$\frac{P_1}{P_2}= (\frac{T_1}{T_2})^{\frac{n}{n-1}}$

$\frac{1}{5}= (\frac{290}{T_2})^{\frac{1.3}{1.3-1}}$

$T_2=420.9 K$

work done in polytropic process

$W=\frac{nR \Delta T }{n-1}= \frac{1.3 \times 8.314\times 130.899}{.3}=4708.62 J$

Now heat transfer relation is

$\Delta Q= \Delta U+ \Delta W$

$\Delta Q= nC_vdT+W$

$\Delta Q= 0.723\times 230.9 + 4708.62$

Heat transfer is Q=4875.56 J