Known Ammonia is heated at constant pressure in a vertical piston–cylinder assembly from the saturated vapor state to a known final temperature.
Find Show the initial and final states on T–υ and p–υ diagrams, and determine the volume at each end state and the work for the process.
Schematic and Given Data:
Engineering Model
1. The ammonia is a closed system.
2. States 1 and 2 are equilibrium states.
3. The process occurs at constant pressure.
4. The piston is the only work mode.
Analysis The initial state is a saturated vapor condition at 20 \text { lbf/in. }^{2} Since the process occurs at constant pressure, the final state is in the superheated vapor region and is fixed by p_{2}=20 lbf / in ^{2} and T_{2}=77^{\circ} F. The initial and final states are shown on the T–υ and p–υ diagrams above.
a. The volumes occupied by the ammonia at states 1 and 2 are obtained using the given mass and the respective specific volumes. From Table A-15E at p_{1}=20 lbf / in .{ }^{2}, and corresponding to Sat. in the temperature column, we get v_{1}=v_{ g }=13.497 ft ^{3} / lb. Thus,
V_{1}=m v_{1}=(0.1 lb )\left(13.497 ft ^{3} / lb \right)
=1.35 ft ^{3}
Interpolating in Table A-15E at p_{2}=20 lbf / in .^{2} \text { and } T_{2}=77^{\circ} F, we get v_{2}=16.7 ft ^{3} / lb. Thus,
V_{2}=m v_{2}=(0.1 lb )\left(16.7 ft ^{3} / lb \right)=1.67 ft ^{3}
b. In this case, the work can be evaluated using Eq. 2.17. Since the pressure is constant
W=\int_{V_{1}}^{V_{2}} p d V (2.17)
W=\int_{V_{1}}^{V_{2}} p d V=p\left(V_{2}-V_{1}\right)
Inserting values
1 \begin{aligned}W &=\left(20 lbf / in .^{2}\right)(1.67-1.35) ft ^{3}\left|\frac{144 in .^{2}}{1 ft ^{2}} \right| \left|\frac{1 Btu }{778 ft \cdot lbf }\right| \\&=1.18 Btu\end{aligned}
1 Note the use of conversion factors in this calculation.
Skills Developed
Ability to…
• define a closed system and identify interactions on its boundary.
• sketch T–υ and p–υ diagrams and locate states on them.
• evaluate work using Eq. 2.17.
• retrieve property data for ammonia at vapor states.
Quick Quiz
If heating continues at 20 \text { lbf/in. }^{2} \text { from } T_{2}=77^{\circ} F \text { to } T_{3}=90^{\circ} F, determine the work for Process 2–3, in Btu. Ans. 0.15 Btu.
