<trans-title xml:lang="en">Theoretical study on thermodynamic properties of NO gas</trans-title>

Jun Jian; Jiao Lei; Qun-Chao Fan; Zhi-Xiang Fan; Jie Ma; Jia Fu; Hui-Dong Li; Yong-Gen Xu

doi:10.7498/aps.69.20191723

Acta Physica Sinica, Volume. 69, Issue 5, 053301-1(2020)

Theoretical study on thermodynamic properties of NO gas

Jun Jian¹, Jiao Lei¹, Qun-Chao Fan^1、*, Zhi-Xiang Fan^1、*, Jie Ma², Jia Fu¹, Hui-Dong Li¹, and Yong-Gen Xu¹

Author Affiliations

¹Key Laboratory of High Performance Scientific Computation, School of Science, Xihua University, Chengdu 610039, China

²State Key Laboratory of Quantum Optics and Quantum Optics Devices, College of Physics and Electronics Engineering, Shanxi University, Taiyuan 030006, China

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Figures & Tables(6)

Fig. 1. Comparison between the VAM full vibrational energies and experimental ones

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Fig. 2. Comparison of the relative errors of different heat capacities

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Table 1. Comparison of different vibrational levels of NO in the ground state (in cm^–1).

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Table 1. Comparison of different vibrational levels of NO in the ground state (in cm^–1).

$\upsilon $	$E_{\rm{\upsilon }}^{{\rm{exp}}}$^[17]	$E_{\rm{\upsilon }}^{{\rm{MCSCF}}}$^[16]	$E_{\rm{\upsilon }}^{{\rm{VAM}}}$	$E_{\rm{\upsilon }}^{{\rm{exp}}} - E_{\rm{\upsilon }}^{{\rm{MCSCF}}}$	$E_{\rm{\upsilon }}^{{\rm{exp}}} - E_{\rm{\upsilon }}^{{\rm{VAM}}}$	υ	$E_{\rm{\upsilon }}^{{\rm{VAM}}}$
注:$E_{\rm{\upsilon }}^{{\rm{VAM}}}$中表示VAM计算所需的已知实验振动能级用黑体标出.
0	948.50	948.60	948.50	–0.10	0	26	40240.70
1	2824.50	2824.60	2824.50	–0.10	0	27	41310.84
2	4627.30	4672.40	4672.27	–45.10	–44.97	28	42340.94
3	6491.90	6492.10	6491.90	–0.20	0	29	43329.70
4	8283.50	8283.90	8283.43	–0.40	0.07	30	44275.74
5	10046.90	10047.80	10046.90	–0.90	0	31	45177.59
6	11782.30	11783.70	11782.30	–1.40	0	32	46033.69
7	13489.40	13491.70	13489.60	–2.30	–0.20	33	46842.41
8		15171.80	15168.73			34	47602.00
9		16823.90	16819.60			35	48310.62
10		18448.00	18442.06			36	48966.35
11		20044.00	20035.93			37	49567.15
12		21611.80	21600.99			38	50110.90
13		23151.30	23136.97			39	50595.35
14		24662.40	24643.56			40	51018.15
15		26144.80	26120.38			41	51376.86
16		27598.50	27567.04			42	51668.92
17		29023.20	28983.04			43	51891.64
18			30367.88			44	52042.23
19			31720.95
20			33041.62
21			34329.18
22			35582.84
23			36801.78
24			37985.07
25			39131.73
$D_{\rm{e}}^{{\rm{exp}}}$	52155.68					$D_{\rm{e}}^{{\rm{cal}}}$	52155.68

Table 2. Calculated molar internal energy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K^–1·mol^–1).

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Table 2. Calculated molar internal energy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K^–1·mol^–1).

T/K	$U_{{\rm{RKR}}}^{{\rm{cal}}}$	$U_{{\rm{MCSCF}}}^{{\rm{cal}}}$	$U_{{\rm{SHO}}}^{{\rm{cal}}}$	$U_{{\rm{VAM}}}^{{\rm{cal}}}$
1000	21.28	21.28	21.27	21.28
1100	22.61	22.61	22.59	22.61
1200	23.98	23.99	23.95	23.98
1300	25.39	25.40	25.34	25.39
1400	26.84	26.84	26.77	26.84
1500	28.31	28.31	28.23	28.31
1600	29.80	29.80	29.70	29.80
1700	31.31	31.31	31.20	31.31
1800	32.84	32.84	32.71	32.84
1900	34.38	34.39	34.24	34.38
2000	35.94	35.94	35.77	35.94
2100	37.51	37.51	37.32	37.51
2200	39.09	39.09	38.88	39.09
2300	40.68	40.68	40.45	40.68
2400	42.28	42.28	42.03	42.28
2500	43.89	43.89	43.61	43.89
2600	45.50	45.50	45.19	45.50
2700	47.12	47.12	46.79	47.12
2800	48.75	48.75	48.38	48.75
2900	50.38	50.38	49.99	50.38
3000	52.01	52.01	51.59	52.01
3100	53.66	53.65	53.20	53.66
3200	55.30	55.30	54.81	55.30
3300	56.95	56.95	56.43	56.95
3400	58.60	58.60	58.05	58.60
3500	60.26	60.26	59.67	60.26
3600	61.92	61.92	61.29	61.92
3700	63.58	63.58	62.91	63.59
3800	65.25	65.24	64.54	65.25
3900	66.91	66.91	66.17	66.92
4000	68.58	68.58	67.80	68.60
4100	70.26	70.25	69.43	70.27
4200	71.93	71.93	71.07	71.95
4300	73.61	73.61	72.70	73.63
4400	75.29	75.28	74.34	75.32
4500	76.97	76.96	75.97	77.01
4600	78.65	78.64	77.61	78.69
4700	80.33	80.32	79.25	80.39
4800	82.01	82.01	80.89	82.08
4900	83.69	83.69	82.53	83.78
5000	85.38	85.37	84.17	85.48

Table 3. Calculated molar entropy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K^–1·mol^–1).

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Table 3. Calculated molar entropy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K^–1·mol^–1).

T/K	$S_{{\rm{RKR}}}^{{\rm{cal}}}$	$S_{{\rm{MCSCF}}}^{{\rm{cal}}}$	$S_{{\rm{SHO}}}^{{\rm{cal}}}$	$S_{{\rm{VAM}}}^{{\rm{cal}}}$
1000	60.50	60.50	60.42	60.50
1100	61.76	61.76	61.67	61.76
1200	62.96	62.96	62.86	62.96
1300	64.09	64.09	63.97	64.09
1400	65.16	65.16	65.03	65.16
1500	66.17	66.17	66.03	66.17
1600	67.13	67.13	66.99	67.13
1700	68.05	68.05	67.89	68.05
1800	68.92	68.92	68.76	68.92
1900	69.76	69.76	69.58	69.76
2000	70.56	70.56	70.37	70.56
2100	71.32	71.32	71.13	71.32
2200	72.06	72.06	71.85	72.06
2300	72.77	72.77	72.55	72.77
2400	73.45	73.45	73.22	73.45
2500	74.10	74.10	73.87	74.10
2600	74.73	74.73	74.49	74.73
2700	75.35	75.35	75.09	75.35
2800	75.94	75.94	75.67	75.94
2900	76.51	76.51	76.23	76.51
3000	77.06	77.06	76.78	77.06
3100	77.60	77.60	77.30	77.60
3200	78.12	78.12	77.82	78.12
3300	78.63	78.63	78.31	78.63
3400	79.12	79.12	78.80	79.13
3500	79.60	79.60	79.27	79.61
3600	80.07	80.07	79.72	80.07
3700	80.53	80.53	80.17	80.53
3800	80.97	80.97	80.60	80.97
3900	81.41	81.40	81.03	81.41
4000	81.83	81.83	81.44	81.83
4100	82.24	82.24	81.84	82.25
4200	82.65	82.64	82.24	82.65
4300	83.04	83.04	82.62	83.05
4400	83.43	83.42	83.00	83.43
4500	83.80	83.80	83.36	83.81
4600	84.17	84.17	83.72	84.18
4700	84.53	84.53	84.08	84.55
4800	84.89	84.89	84.42	84.90
4900	85.24	85.23	84.76	85.25
5000	85.58	85.57	85.09	85.60

Table 4. Comparisons of different molar capacities with observed experimental (in J·K^–1·mol^–1).

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Table 4. Comparisons of different molar capacities with observed experimental (in J·K^–1·mol^–1).

T/K	${C_{{\rm{exp}}}}$	$C_{{\rm{RKR}}}^{{\rm{cal}}}$	$C_{{\rm{MCSCF}}}^{{\rm{cal}}}$	$C_{{\rm{SHO}}}^{{\rm{cal}}}$	$C_{{\rm{VAM}}}^{{\rm{cal}}}$	${\delta _{{\rm{RKR}}}}$^a	${\delta _{{\rm{MCSCF}}}}$^b	${\delta _{{\rm{SHO}}}}$^c	${\delta _{{\rm{VAM}}}}$^d
注: a, ${\delta _{{\rm{RKR}}}} = \left\| {C_{{\rm{exp}}}^{} - C_{{\rm{RKR}}}^{{\rm{cal}}}} \right\|/C_{{\rm{exp}}}^{} \times 100\% $; b, ${\delta _{{\rm{MCSCF}}}} = \left\| {C_{{\rm{exp}}}^{} - C_{{\rm{MCSCF}}}^{{\rm{cal}}}} \right\|/C_{{\rm{exp}}}^{} \times 100\% $; c, $ {\delta _{{\rm{SHO}}}} = \left\| {C_{{\rm{exp}}} - C_{{\rm{SHO}}}^{{\rm{cal}}}} \right\|/C_{{\rm{exp}}} \times 100\% $; d, $ {\delta _{{\rm{VAM}}}} = \left\| {C_{{\rm{exp}}} - C_{{\rm{VAM}}}^{{\rm{cal}}}} \right\|/C_{{\rm{exp}}} \times 100\% .$
1000	13.20	13.04	13.04	10.72	13.04	1.22%	1.22%	18.82%	1.22%
1100	13.68	13.52	13.52	11.24	13.52	1.18%	1.18%	17.85%	1.18%
1200	14.09	13.93	13.93	11.73	13.93	1.16%	1.16%	16.77%	1.16%
1300	14.44	14.27	14.27	12.17	14.27	1.17%	1.17%	15.69%	1.17%
1400	14.74	14.56	14.56	12.58	14.56	1.19%	1.19%	14.66%	1.19%
1500	14.99	14.81	14.81	12.94	14.81	1.21%	1.21%	13.70%	1.21%
1600	15.22	15.03	15.03	13.26	15.03	1.23%	1.23%	12.83%	1.23%
1700	15.41	15.22	15.21	13.55	15.22	1.26%	1.26%	12.04%	1.26%
1800	15.58	15.38	15.38	13.81	15.38	1.29%	1.29%	11.35%	1.29%
1900	15.73	15.52	15.52	14.04	15.52	1.33%	1.33%	10.73%	1.33%
2000	15.86	15.65	15.64	14.25	15.65	1.36%	1.37%	10.18%	1.36%
2100	15.98	15.76	15.76	14.43	15.76	1.41%	1.41%	9.71%	1.41%
2200	16.09	15.86	15.86	14.59	15.86	1.45%	1.45%	9.29%	1.45%
2300	16.18	15.95	15.94	14.74	15.95	1.48%	1.49%	8.92%	1.48%
2400	16.27	16.03	16.03	14.88	16.03	1.52%	1.53%	8.59%	1.52%
2500	16.35	16.10	16.10	15.00	16.10	1.56%	1.57%	8.31%	1.56%
2600	16.43	16.17	16.17	15.10	16.17	1.61%	1.61%	8.07%	1.61%
2700	16.50	16.23	16.23	15.20	16.23	1.65%	1.65%	7.85%	1.65%
2800	16.56	16.28	16.28	15.29	16.28	1.69%	1.70%	7.67%	1.69%
2900	16.62	16.34	16.33	15.38	16.34	1.74%	1.74%	7.51%	1.73%
3000	16.68	16.38	16.38	15.45	16.39	1.77%	1.78%	7.37%	1.77%
3100	16.73	16.43	16.43	15.52	16.43	1.82%	1.83%	7.25%	1.80%
3200	16.78	16.47	16.47	15.58	16.47	1.87%	1.88%	7.16%	1.85%
3300	16.83	16.51	16.51	15.64	16.51	1.91%	1.92%	7.08%	1.88%
3400	16.88	16.55	16.54	15.69	16.55	1.96%	1.97%	7.01%	1.92%
3500	16.92	16.58	16.58	15.74	16.59	2.01%	2.02%	6.96%	1.95%
3600	16.96	16.61	16.61	15.79	16.62	2.06%	2.07%	6.91%	1.99%
3700	17.00	16.64	16.64	15.83	16.66	2.12%	2.13%	6.89%	2.03%
3800	17.04	16.67	16.67	15.87	16.69	2.18%	2.19%	6.86%	2.06%
3900	17.08	16.69	16.69	15.91	16.72	2.24%	2.25%	6.85%	2.09%
4000	17.11	16.72	16.71	15.94	16.75	2.31%	2.32%	6.85%	2.13%
4100	17.15	16.74	16.74	15.97	16.78	2.38%	2.40%	6.86%	2.16%
4200	17.18	16.76	16.75	16.00	16.81	2.46%	2.48%	6.86%	2.18%
4300	17.21	16.77	16.77	16.03	16.83	2.55%	2.57%	6.88%	2.21%
4400	17.24	16.79	16.79	16.05	16.86	2.64%	2.66%	6.90%	2.24%
4500	17.28	16.80	16.80	16.08	16.89	2.74%	2.76%	6.93%	2.26%
4600	17.31	16.81	16.81	16.10	16.91	2.85%	2.86%	6.96%	2.29%
4700	17.34	16.82	16.82	16.12	16.94	2.96%	2.99%	7.00%	2.31%
4800	17.36	16.83	16.83	16.14	16.96	3.09%	3.11%	7.04%	2.32%
4900	17.39	16.83	16.83	16.16	16.99	3.22%	3.25%	7.08%	2.35%
5000	17.42	16.84	16.83	16.18	17.01	3.37%	3.38%	7.13%	2.36%

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Jun Jian, Jiao Lei, Qun-Chao Fan, Zhi-Xiang Fan, Jie Ma, Jia Fu, Hui-Dong Li, Yong-Gen Xu. Theoretical study on thermodynamic properties of NO gas[J]. Acta Physica Sinica, 2020, 69(5): 053301-1

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Paper Information

Category:

Received: Nov. 11, 2019

Accepted: --

Published Online: Nov. 18, 2020

The Author Email: Fan Zhi-Xiang (fanzhixiang235@126.com)

DOI:10.7498/aps.69.20191723

Topics

Nuclear physics

Particles and fields

Particle and nuclear astrophysics and cosmology

Table 1. Comparison of different vibrational levels of NO in the ground state (in cm–1).

Table 1. Comparison of different vibrational levels of NO in the ground state (in cm–1).

Table 2. Calculated molar internal energy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K–1·mol–1).

Table 2. Calculated molar internal energy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K–1·mol–1).

Table 3. Calculated molar entropy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K–1·mol–1).

Table 3. Calculated molar entropy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K–1·mol–1).

Table 4. Comparisons of different molar capacities with observed experimental (in J·K–1·mol–1).

Table 4. Comparisons of different molar capacities with observed experimental (in J·K–1·mol–1).

Table 1. Comparison of different vibrational levels of NO in the ground state (in cm^–1).

Table 1. Comparison of different vibrational levels of NO in the ground state (in cm^–1).

Table 2. Calculated molar internal energy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K^–1·mol^–1).

Table 2. Calculated molar internal energy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K^–1·mol^–1).

Table 3. Calculated molar entropy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K^–1·mol^–1).

Table 3. Calculated molar entropy using RKR, MCSCF, SHO, and VAM vibrational energies as the vibrational contributions, respectively (in J·K^–1·mol^–1).

Table 4. Comparisons of different molar capacities with observed experimental (in J·K^–1·mol^–1).

Table 4. Comparisons of different molar capacities with observed experimental (in J·K^–1·mol^–1).