Question 12.7: First Law of Thermodynamics: Closed System A closed tank of ......

Heating and Cooling of Buildings Principles and Practice of Energy Efficient Design [1026599]

First Law of Thermodynamics: Closed System

A closed tank of refrigerant R22 has a volume of 700 ft³ and is filled with 2800 $lb_{m}$ of a wet mixture of R22 at an initial pressure of 136.19 psia. The tank is moved outdoors and absorbs sufficient solar heat to cause saturated vapor alone to exist within the tank. What is the thermodynamic state (temperature, specific volume, and pressure) prior to the addition of heat?
What are the nal temperature and pressure values after heating?
Given: V, m, $p_{ini}$
Find: $v_{ini}, p_{final}, T_{final}$
Lookup values: The R22 table (Table A5) is used.

TABLE A.5 (IP Units) Properties of Saturated Liquid and Saturated Vapor of R-22
Temp. (°F)	Pressure (psia)	Density (lb/ft³)	Volume (ft³/lb)	Enthalpy (Btu/lb)		Entropy (Btu/lb · °F)
Temp. (°F)	Pressure (psia)	Liquid	Vapor	Liquid	Vapor	Liquid	Vapor
-250	—	107.37	—	-63.169	76.604	-0.21914	0.44952
-240	—	106.41	—	-56.462	77.629	-0.18786	0.42332
-230	—	105.48	—	-51.569	78.669	-0.16605	0.40101
-220	0.002	104.58	16805	-47.705	79.724	-0.14958	0.38211
-210	0.004	103.7	6982.6	-44.426	80.796	-0.13616	0.36538
-200	0.01	102.81	3151.5	-41.474	81.882	-0.12457	0.35048
-190	0.022	101.92	1527.4	-38.706	82.984	-0.11411	0.33715
-180	0.044	101.03	787.79	-36.038	84.1	-0.10439	0.32518
-170	0.084	100.12	429.22	-33.424	85.23	-0.09521	0.31441
-160	0.151	99.22	245.51	-30.839	86.373	-0.08644	0.3047
-150	0.262	98.3	146.65	-28.269	87.528	-0.078	0.29594
-140	0.435	97.38	91.059	-25.708	88.692	-0.06986	0.28801
-130	0.696	96.46	58.544	-23.15	89.864	-0.06198	0.28082
-120	1.08	95.53	38.833	-20.594	91.04	-0.05435	0.2743
-110	1.626	94.6	26.494	-18.038	92.218	-0.04694	0.26838
-100	2.384	93.66	18.54	-15.481	93.397	-0.03973	0.26298
-90	3.413	92.71	13.275	-12.921	94.572	-0.03271	0.25807
-80	4.778	91.75	9.7044	-10.355	95.741	-0.02587	0.25357
-70	6.555	90.79	7.2285	-7.783	96.901	-0.01919	0.24945
-60	8.83	89.81	5.4766	-5.201	98.049	-0.01266	0.24567
-50	11.696	88.83	4.2138	-2.608	99.182	-0.00627	0.2422
-45	13.383	88.33	3.716	-1.306	99.742	-0.00312	0.24056
−41.44	14.696	87.97	3.4048	−0.377	100.138	−0.0009	0.23944
-40	15.255	87.82	3.288	0	100.296	0	0.23899
-35	17.329	87.32	2.9185	1.31	100.847	0.00309	0.23748
-30	19.617	86.81	2.5984	2.624	101.391	0.00616	0.23602
-25	22.136	86.29	2.3202	3.944	101.928	0.0092	0.23462
-20	24.899	85.77	2.0774	5.268	102.461	0.01222	0.23327
-15	27.924	85.25	1.865	6.598	102.986	0.01521	0.23197
-10	31.226	84.72	1.6784	7.934	103.503	0.01818	0.23071
-5	34.821	84.18	1.5142	9.276	104.013	0.02113	0.22949
0	38.726	83.64	1.3691	10.624	104.515	0.02406	0.22832
5	42.96	83.09	1.2406	11.979	105.009	0.02697	0.22718
10	47.538	82.54	1.1265	13.342	105.493	0.02987	0.22607
15	52.48	81.98	1.025	14.712	105.968	0.03275	0.225
20	57.803	81.41	0.9343	16.09	106.434	0.03561	0.22395
25	63.526	80.84	0.8532	17.476	106.891	0.03846	0.22294
30	69.667	80.26	0.7804	18.871	107.336	0.04129	0.22195
35	76.245	79.67	0.715	20.275	107.769	0.04411	0.22098
40	83.28	79.07	0.6561	21.688	108.191	0.04692	0.22004
45	90.791	78.46	0.6029	23.111	108.6	0.04972	0.21912
50	98.799	77.84	0.5548	24.544	108.997	0.05251	0.21821
55	107.32	77.22	0.5111	25.988	109.379	0.05529	0.21732
60	116.38	76.58	0.4715	27.443	109.748	0.05806	0.21644
65	126	75.93	0.4355	28.909	110.103	0.06082	0.21557
70	136.19	75.27	0.4026	30.387	110.441	0.06358	0.21472
75	146.98	74.6	0.3726	31.877	110.761	0.06633	0.21387
80	158.4	73.92	0.3451	33.381	111.066	0.06907	0.21302
85	170.45	73.22	0.3199	34.898	111.35	0.07182	0.21218
90	183.17	72.51	0.2968	36.43	111.616	0.07456	0.21134
95	196.57	71.79	0.2756	37.977	111.859	0.0773	0.2105
100	210.69	71.05	0.256	39.538	112.081	0.08003	0.20965
105	225.53	70.29	0.2379	41.119	112.278	0.08277	0.20879
110	241.14	69.51	0.2212	42.717	112.448	0.08552	0.20793
115	257.52	68.71	0.2058	44.334	112.591	0.08827	0.20705
120	274.71	67.89	0.1914	45.972	112.704	0.09103	0.20615
125	292.73	67.05	0.1781	47.633	112.783	0.09379	0.20522
130	311.61	66.17	0.1657	49.319	112.825	0.09657	0.20427
135	331.38	65.27	0.1542	51.032	112.826	0.09937	0.20329
140	352.07	64.33	0.1434	52.775	112.784	0.1022	0.20227
145	373.71	63.35	0.1332	54.553	112.692	0.10504	0.20119
150	396.32	62.33	0.1237	56.37	112.541	0.10793	0.20006
160	444.65	60.12	0.1063	60.145	112.035	0.11383	0.19757
170	497.35	57.59	0.0907	64.175	111.165	0.12001	0.19464
180	554.82	54.57	0.0763	68.597	109.753	0.12668	0.19102
190	617.53	50.62	0.0625	73.742	107.398	0.13432	0.18613
200	686.11	44.44	0.0478	80.558	102.809	0.14432	0.17805
205.06	723.74	32.7	0.0306	91.052	91.052	0.15989	0.15989
Source: Courtesy of ASHRAE, Handbook of Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA, 1997. With permission. Notes: Values shown in italics are at the boiling point. Values shown in bold are at the critical point.

TABLE A.5 (SI Units) Properties of Saturated Liquid and Saturated Vapor of R-22
Temp. (°C)	Pressure (MPa)	Density (kg/m³)	Volume (m³/kg)	Enthalpy (kJ/kg)		Entropy (kJ/kg · K)
Temp. (°C)	Pressure (MPa)	Liquid	Vapor	Liquid	Vapor	Liquid	Vapor
-150.00	—	1701.5	—	26.01	335.85	0.0566	2.5752
-140.00	—	1675.3	—	43.84	340.24	0.1961	2.4222
-130.00	0.00006	1649.7	229.29	57.00	344.75	0.2916	2.3017
-120.00	0.00023	1624.0	63.648	68.51	349.38	0.3694	2.2033
-110.00	0.00074	1598.0	21.311	79.47	354.11	0.4386	2.1220
-100.00	0.00200	1571.7	8.2980	90.24	358.93	0.5027	2.0545
-90.00	0.00480	1545.1	3.6548	100.95	363.82	0.5629	1.9982
-80.00	0.01035	1518.3	1.7816	111.66	368.75	0.6197	1.9508
-70.00	0.02044	1491.1	0.94476	122.36	373.68	0.6738	1.9109
-60.00	0.03747	1463.6	0.53734	133.11	378.58	0.7253	1.8770
-50.00	0.06449	1435.5	0.32405	143.91	383.39	0.7748	1.8480
-48.00	0.07140	1429.8	0.29469	146.08	384.35	0.7844	1.8427
-46.00	0.07890	1424.1	0.26849	148.25	385.29	0.7940	1.8376
-44.00	0.08700	1418.4	0.24507	150.43	386.23	0.8035	1.8326
-42.00	0.09575	1412.6	0.22410	152.61	387.17	0.8130	1.8277
−40.80	0.10132	1409.1	0.21256	153.93	387.72	0.8186	1.8249
-40.00	0.10518	1406.8	0.20526	154.80	388.09	0.8224	1.8230
-38.00	0.11533	1401.0	0.18832	156.99	389.01	0.8317	1.8184
-36.00	0.12623	1395.1	0.17306	159.19	389.93	0.8410	1.8140
-34.00	0.13793	1389.2	0.15927	161.40	390.84	0.8502	1.8096
-32.00	0.15045	1383.3	0.14680	163.61	391.74	0.8594	1.8054
-30.00	0.16384	1377.3	0.13551	165.82	392.63	0.8685	1.8013
-28.00	0.17815	1371.3	0.12525	168.04	393.52	0.8776	1.7973
-26.00	0.19340	1365.2	0.11593	170.27	394.39	0.8866	1.7934
-24.00	0.20965	1359.1	0.10744	172.51	395.26	0.8955	1.7896
-22.00	0.22693	1352.9	0.09970	174.75	396.12	0.9044	1.7859
-20.00	0.24529	1346.8	0.09262	177.00	396.97	0.9133	1.7822
-18.00	0.26477	1340.5	0.08615	179.26	397.81	0.9222	1.7787
-16.00	0.28542	1334.2	0.08023	181.53	398.64	0.9309	1.7752
-14.00	0.30728	1327.9	0.07479	183.81	399.46	0.9397	1.7719
-12.00	0.33040	1321.5	0.06979	186.09	400.27	0.9484	1.7686
-10.00	0.35482	1315.0	0.06520	188.38	401.07	0.9571	1.7653
-8.00	0.38059	1308.5	0.06096	190.69	401.85	0.9657	1.7621
-6.00	0.40775	1301.9	0.05706	193.00	402.63	0.9743	1.7590
-4.00	0.43636	1295.3	0.05345	195.32	403.39	0.9829	1.7560
-2.00	0.46646	1288.6	0.05012	197.66	404.14	0.9915	1.7530
0.00	0.49811	1281.8	0.04703	200.00	404.87	1.0000	1.7500
2.00	0.53134	1275.0	0.04417	202.35	405.59	1.0085	1.7471
4.00	0.56622	1268.1	0.04152	204.72	406.30	1.0170	1.7443
6.00	0.6028	1261.1	0.03906	207.10	406.99	1.0254	1.7415
8.00	0.6411	1254.0	0.03676	209.49	407.67	1.0338	1.7387
10.00	0.6812	1246.9	0.03463	211.89	408.33	1.0422	1.7360
12.00	0.7231	1239.7	0.03265	214.31	408.97	1.0506	1.7333
14.00	0.767	1232.4	0.03079	216.74	409.60	1.0590	1.7306
16.00	0.8128	1225.0	0.02906	219.18	410.21	1.0673	1.7280
18.00	0.8606	1217.6	0.02744	221.63	410.80	1.0756	1.7254
12.00	0.9104	1210.0	0.02593	224.10	411.38	1.0840	1.7228
22.00	0.9624	1202.4	0.02451	226.59	411.93	1.0923	1.7202
24.00	1.0165	1194.6	0.02319	229.09	412.46	1.1006	1.7177
26.00	1.0728	1186.8	0.02194	231.60	412.98	1.1088	1.7151
28.00	1.1314	1178.8	0.02077	234.14	413.46	1.1171	1.7126
30.00	1.1924	1170.7	0.01968	236.69	413.93	1.1254	1.7101
32.00	1.2557	1162.5	0.01864	239.25	414.37	1.1336	1.7075
34.00	1.3215	1154.2	0.01767	241.84	414.79	1.1419	1.7050
36.00	1.3898	1145.7	0.01675	244.44	415.18	1.1501	1.7024
38.00	1.4606	1137.1	0.01589	247.06	415.54	1.1584	1.6999
40.00	1.5341	1128.4	0.01507	249.71	415.87	1.1667	1.6973
42.00	1.6103	1119.5	0.01430	252.37	416.17	1.1749	1.6947
44.00	1.6892	1110.4	0.01357	255.06	416.44	1.1832	1.6921
46.00	1.7709	1101.2	0.01288	257.77	416.68	1.1915	1.6894
48.00	1.8555	1091.8	0.01223	260.51	416.87	1.1998	1.6867
50.00	1.9431	1082.1	0.01161	263.27	417.03	1.2081	1.6840
55.00	2.1753	1057.1	0.01020	270.31	417.24	1.2291	1.6768
60.00	2.4274	1030.5	0.00895	277.56	417.14	1.2503	1.6692
65.00	2.7008	1001.8	0.00784	285.06	416.65	1.2718	1.6610
70.00	2.9967	970.4	0.00684	292.90	415.69	1.2940	1.6518
75.00	3.3168	935.3	0.00594	301.18	414.09	1.3169	1.6413
80.00	3.6627	894.8	0.00511	310.10	411.60	1.3413	1.6287
85.00	4.0368	845.1	0.00433	320.05	407.72	1.3680	1.6128
90.00	4.4416	777.5	0.00355	331.98	401.33	1.3998	1.5907
95.00	4.8820	665.4	0.00264	348.86	387.46	1.4442	1.5491
96.14	4.9900	523.8	0.00191	366.59	366.59	1.4918	1.4918
Source: Courtesy of ASHRAE, Handbook of Fundamentals, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA, 1997. With permission. Notes: Values shown in italics are at the boiling point. Values shown in bold are at the critical point.

Step-by-Step

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The initial (and final) specic volume is

v = \frac{700  ft^{3}}{2800  lb_{m}} = 0.25  ft^{3}/lb_{m}

From the saturation table for R22 at 136.19 psia, we read that the initial temperature of the tank contents is $T_{i} = 70°F$ .
As heat is added, the wet mixture of R22 becomes saturated vapor. Note that the process is a constant-volume process; hence, one can find the final thermodynamic state by using the saturation tables again.
In the saturated vapor column of the table, we determine the final temperature and pressure directly from the entries corresponding to a saturated vapor value of $0.25 ft³/lb_{m}$ . The values are approximately $T_{final} = 102°F, p_{final} = 216.45 psia$ .

Comments
If needed, one could determine the amount of solar heat absorbed by the tank by finding the difference between the internal energy at the start and end of the process, as indicated by the first law (the work done is zero since the volume is constant):
Q = ΔU
The interested reader can verify that the heat absorbed is approximately 79 kBtu.