Why am I getting 2 different answers with this thermodynamics question? There is

Question

Why am I getting 2 different answers with this thermodynamics question?

There is a sealed piston cylinder device that is adiabatic and has is at 150kPa pressure with a saturated water mixture of u = 1800kJ/kg. There is 1000kJ/kg of work done on the piston. If the final pressure is 300kPa what is the final temperature at state 2.

The first way I tried to solve like this

H = U + pv

H = U + W

H = 1800 kJ/kg + 1000 kJ/kg

H = 2800 kJ/kg

When I look up the Enthalpy at 300kPa and 2800kJ/kg I get a temperature of approximately 200 C

However, when I solve it like this below I got a different answer. Why?

?U = W – Q There is no Q because adiabatic

U2 – U1 = Win

U2 – 1800kJ/kg = 1000kJ/kg

U2 = 2800 kJ/kg

Looking it up in the steam table at 300kPa I get approximately 300 C. Which one is correct and why? Could you explain which one is correct and why I am getting 2 different answers? Both of the formulas I used are correct? I have marked the values on the table I provided.

918 PROPERTY TABLES AND CHARTS TABLE A-6 Superheated water LI LI oC m3/k kJ/ kJ/k kJ/k kJ/kg kJ/kg.K P 0.01 MPa (45.81°C)* P-0.05 MPa (81.32°C) Sat. 14.670 2437.2 2583.9 8.1488 3.2403 2483.2 2645.2 7.5931 50 14.867 2443.3 2592.0 8.1741 100 17.196 2515.5 2687.5 8.4489 3.4187 2511.5 2682.4 7.6953 150 19.513 2587.9 2783.0 8.6893 3.88972585.7 2780.2 7.9413 200 21.826 2661.4 2879.6 8.9049 4.3562 2660.0 2877.8 8.1592 250 24.136 2736.1 2977.5 9.1015 4.8206 2735.1 2976.2 8.3568 300 26.446 2812.3 3076.7 9.2827 5.2841 2811.6 3075.8 8.5387 400 31.063 2969.3 3280.0 9.6094 6.2094 2968.9 3279.3 8.8659 500 35.680 3132.9 3489.7 9.8998 7.1338 3132.6 3489.3 9.1566 600 40.2963303.3 3706.3 10.1631 8.0577 3303.1 3706.0 9.4201 700 44.911 3480.8 3929.9 10.4056 8.9813 3480.6 3929.7 9.6626 800 49.527 3665.4 4160.6 10.6312 9.9047 3665.2 4160.4 9.8883 900 54.143 3856.9 4398.3 10.8429 10.8280 3856.8 4398.2 10.1000 1000 58.758 4055.3 4642.8 11.0429 11.7513 4055.2 4642.7 10.3000 1100 63.373 4260.0 4893.8 11.2326 12.6745 4259.9 4893.7 10.4897 1200 67.989 4470.9 5150.8 11.4132 13.5977 4470.8 5150.7 10.6704 1300 72.604 4687.4 5413.4 11.5857 14.5209 4687.3 5413.3 10.8429 P= 0.20 MPa (120.21°C) ?-0.30 MPa (133.52°C) Sat. 0.88578 2529.1 2706.3 7.1270 0.60582 2543.2 2724.9 6.9917 150 0.95986 2577.1 2769.1 7.2810 0.63402 2571.0 2761.2 7.0792 7.3132 250 1.19890 2731.4 2971.2 7.7100 0.79645 2728.9 2967.9 7.5180 300 1.31623 2808.8 3072.1 7.894 0.87535 2807.0 3069.6 7.7037 3275.5 8.0347 500 1.78142 3131.4 3487.7 8.5153 1.18672 3130.6 3486.6 8.3271 600 2.01302 3302.2 3704.8 8.7793 1.34139 3301.6 3704.0 8.5915 700 2.244343479.9 3928.8 9.0221 1.49580 3479.5 3928.2 8.8345 800 2.47550 3664.7 4159.8 9.2479 1.65004 3664.3 4159.3 9.0605 900 2.70656 3856.3 4397.7 9.4598 1.80417 3856.0 4397.3 9.2725 1000 2.93755 4054.8 4642.3 9.6599 1.95824 4054.5 4642.0 9.4726 1100 3.16848 4259.6 4893.3 9.8497 2.11226 4259.4 4893.1 9.6624 1200 3.39938 4470.5 5150.4 10.0304 2.26624 4470.3 5150.2 9.8431 1300 3.63026 4687.1 5413.1 10.2029 2.42019 4686.9 5413.0 10.0157 200 1.08049 2654.6 2870.7 7.508 0.71643 2651.0 286 400 1.549342967.2 3277.0 8.2236 1.03155

Explanation / Answer

It is recommended to follow the second procedure to approach the given problem.

Use only the second formula because the in the first formula of H=U+PV, the term PV becomes the work only in the case of the flow work, and in that too the work is (Pv) where v is the specific volume. Only, the second formula you have mentioned in your answer is valid at all times.

Also, I think that you are aware of the general sign convention. According to the sign convention, the work done on the system is negative.

So, from the First Law of Thermodynamics

Q-W=U

But as an adiabatic process,

Q=0,

Thus, the equation is reduced to the form.

-W=U

-(-1000)=U2-U1

U2-U1=1000

U2=1000+1800

U2=2800 kJ/kg

So, for the corresponding value of U from the steam table, the temperature should be approx. 300 degree Celcius

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.