## Related questions with answers

An air compressor is used to charge an initially empty 200-L tank with air up to 5 MPa. The air inlet to the compressor is at 100 kPa, 17$^{\circ} \mathrm{C}$ and the compressor’s isentropic efficiency is 80%. Find the total compressor work and the change in exergy of the air.

Solutions

Verified$\textbf{Given:}$

Substance: $Air$

$V=0.2 m^3$

$p_2=5000$ kPa

$p_i=100$ kPa

$T_i=290.15$ K

$\eta_C=0.8$

$\textbf{Required:}$ $_1W_2^{ac}=?;\Phi=?$

We are given following data for initially empty tank charged with air compressor:

$V=200\text{ L}=0.2\text{ m}^3$

$T_{1}=290\text{ K}$

$P_1=100\text{ kPa}$

$P_2=5000\text{ kPa}$

$\eta=0.8$

From Properties table A.5. we can find Air gas constant:

$R=0.287\frac{\text{ kJ}}{\text{ kg K}}$

From Ideal Gas Properties of Air table A.7.1. corresponding to $T_1=290\text{ K}$ we can find stage 1 specific standard entropy and enthalpy:

$h_1=290.43\frac{\text{ kJ}}{\text{ kg}}$

$s_T^0=6.83521\frac{\text{ kJ}}{\text{ kg K}}$

Calculating stage 1 specific entropy:

$s_1=s_T^0+R\cdot \ln{\dfrac{P_2}{P_1}}=6.83521+0.287\cdot \ln{\dfrac{5000}{100}}=7.9580\frac{\text{ kJ}}{\text{ kg K}}$

There is no change in entropy in isentropic process:

$s_2=s_1=7.9580\frac{\text{ kJ}}{\text{ kg K}}$

From Ideal Gas Properties of Air table A.7.1. corresponding to $s_2\approx 7.9521\frac{\text{ kJ}}{\text{ kg K}}$ we can find stage 2 specific enthalpy:

$h_2=877.40\frac{\text{ kJ}}{\text{ kg}}$

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Fundamentals of Electric Circuits

6th Edition•ISBN: 9780078028229 (2 more)Charles Alexander, Matthew Sadiku#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th Edition•ISBN: 9780133942651 (8 more)Randall D. Knight#### Advanced Engineering Mathematics

10th Edition•ISBN: 9780470458365 (5 more)Erwin Kreyszig#### Fundamentals of Thermodynamics

8th Edition•ISBN: 9781118131992Claus Borgnakke, Richard E. Sonntag## More related questions

1/4

1/7