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3 years ago

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Air is compressed in an isentropic process from an initial pressure and temperature of P1 = 90 kPa and T1=22°C to a final pressu

re of P2=900 kPa. Determine: a)- The final temperature of the air. b)-The work done per kg of air during the process.

1 answer:

ivolga24 [154]3 years ago

4 0

Answer:

a) $T_2=569.35 K$

b)Work done per kg of air=196.84 KJ/Kg

Explanation:

Given: $\gamma =1.4$ for air.

$P_1=90 KPa ,T_=22^\circ C,P_2=900 KPa$

We know that

$\dfrac{T_2}{T_1}=\left (\frac{P_2}{P_1}\right )^{\dfrac{{\gamma-1}}{\gamma}}$

So $\dfrac{T_2}{295}=\left (\frac{900}{90}\right )^{\dfrac{{1.4-1}}{1.4}}$

$T_2=569.35 K$

(a) $T_2=569.35 K$

(b)Work for adiabatic process

W= $\frac{P_1V_1-P_2V_2}{\gamma -1}$

We know that PV=mRT for ideal gas.

W= $mR\frac{T_1-T_2}{\gamma -1}$

Now by putting values

work per kg of air= $0.287\times \frac{295-569.35}{1.4 -1}$

Work w=-196.84 KJ/Kg (Negative sign indicate work given to input.)

So work done per kg of air=196.84 KJ/Kg

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