Question

1.85 kg of N2 gas (an ideal diatomic gas) is contained in a piston-cylinder device having pressure of 185 kPa and temperature of 18.5°C. The gas is now compressed slowly in a polytropic process during which pV135 = constant. The process ends when the volume is reduced to 0.85 times the original volume. The entropy change of N2 gas during this process is …. J/K

Answer 1

Answer:

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Answer 2

Given,

$P_1$ = 185 kPa

$T_1$ = 18.5°C = 291.5 K

m = 1.85 kg

n = 1.35

$V_2$ = 0.85 $V_1$

To find,

The entropy change during this process.

Solution,

The gas constant of $N_2$, R =0.296 kPa$m^3$/kg K

The given system is a closed system.

The final temperature and pressure of nitrogen are,

$P_2V_2^{1.35} = P_1V^{1.35}_1$

$P_2 = (V_1/V_2)^{1.35}P_1$

    = $V_1(0.85V_1)^{1.35}185 =$ 148.55 kPa

Now,

P$_1$V$_1$/T$_1$ = P$_2$V$_2$/T$_2$

T$_2$ = (P$_2$V$_2$/P$_1$V$_1$)T$_1$

    = (148.55×0.85/185)×291.5

    = 198.95 K

now,

change in entropy, ΔS (for polytropic process)

= C$_v$lnT$_2$/T$_1$ + RlnV$_2$/V$_1$

= -0.382 - 0.05

= -0.432 J/K