Try the fastest way to create flashcards

A cylinder having an initial volume of 100 ft3 contains 0.2 lbm of water at 100 F. The water is then compressed in an isothermal quasi-equilibrium process until it has a quality of 50%. Calculate the work done in the process, assuming that water vapor is an ideal gas.


Step 1
1 of 3

We are given following data for Water:

T1=100 FT_{1}=100\text{ F}

m=0.2 lbmm=0.2\text{ lbm}

V1=100 ft3V_1=100\text{ ft}^3


From Saturated Water table F.7.1. corresponding to T=100 FT=100\text{ F} we can obtain stage 2 specific volume and pressure:

ν2=νg=349.9764 ft3 lbm\nu_{2}=\nu_g=349.9764\frac{\text{ ft}^3}{\text{ lbm}}

P2=Pg=0.95 lbf in2P_2=P_g=0.95\frac{\text{ lbf}}{\text{ in}^2}

Initial specific volume and pressure are equal to:

ν1=V1m=1000.2=500 ft3 lbm\nu_1=\dfrac{V_1}{m}=\dfrac{100}{0.2}=500\frac{\text{ ft}^3}{\text{ lbm}}

P1=P2ν2ν1=0.95349.9764500=0.665 lbf in2P_1=\dfrac{P_2\cdot \nu_2}{\nu_1}=\dfrac{0.95\cdot 349.9764}{500}=0.665\frac{\text{ lbf}}{\text{ in}^2}

Stage 2 volume is equal to:

V2=mν2=0.2349.9764=70 ft3V_2=m\cdot \nu_2=0.2\cdot 349.9764=70\text{ ft}^3

We can now calculate stage 1-2 work:

W12=PdV=P1V1dVV=P1V1lnV2V1=0.665144100778ln70100=4.39 Btu\begin{align*} W_{1-2}&=\int PdV=P_1\cdot V_1\cdot \int \dfrac{dV}{V}=P_1\cdot V_1\cdot \ln \dfrac{V_2}{V_1}\\\\ &=\dfrac{0.665\cdot 144\cdot 100}{778}\cdot \ln \dfrac{70}{100}\\\\ &=-4.39\text{ Btu} \end{align*}

Create a free account to view solutions

Create a free account to view solutions

Recommended textbook solutions

Fundamentals of Electric Circuits 6th Edition by Charles Alexander, Matthew Sadiku

Fundamentals of Electric Circuits

6th EditionISBN: 9780078028229 (2 more)Charles Alexander, Matthew Sadiku
2,120 solutions
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics 4th Edition by Randall D. Knight

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (8 more)Randall D. Knight
3,508 solutions
Advanced Engineering Mathematics 10th Edition by Erwin Kreyszig

Advanced Engineering Mathematics

10th EditionISBN: 9780470458365 (5 more)Erwin Kreyszig
4,134 solutions
Fundamentals of Thermodynamics 8th Edition by Claus Borgnakke, Richard E. Sonntag

Fundamentals of Thermodynamics

8th EditionISBN: 9781118131992Claus Borgnakke, Richard E. Sonntag
2,812 solutions

More related questions