{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 4.6 – Steam Tables\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.6.0 – Learning Objectives\n", "\n", "By the end of this section you should be able to:\n", "\n", "1. Understand what steam tables tell us.\n", "2. Use steam tables to solve thermodynamic problems.\n", "3. Interpolate between data points.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.6.1 – Introduction\n", "\n", "Water, and in specific, steam is used in many processes. Most commonly, it is used in the transfer of energy. Because of this, scientist and engineers have created extensive data tables on a variety of conditions.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.6.2 – Table Description\n", "\n", "Shown below is a saturated steam table. A **saturated steam table** will include data of both the liquid and vapour phases of water at a given temperature and pressure." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/html": [ "
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Temperature (C)Pressure (MPa)Volume (l, m3/kg)Volume (v, m3/kg)Internal Energy (l, kJ/kg)Δ Internal Energy of Vapourization (kJ/kg)Internal Energy (v, kJ/kg)Enthalpy (l, kJ/kg)Δ Enthalpy of Vapourization (kJ/kg)Enthalpy (v, kJ/kg)Entropy (l, J/g*K)Δ Entropy of Vapourization (kJ/kg)Entropy (v, J/g*K)
00.010.0006120.001000205.99000.0002374.9002374.90.0002500.9002500.90.0000009.1555009.1555
15.000.0008730.001000147.010021.0192360.7812381.821.0202489.0802510.10.0762548.9485469.0248
210.000.0012280.001000106.300042.0202346.5802388.642.0212477.1792519.20.1510908.7487108.8998
315.000.0017060.00100177.875062.9802332.5202395.562.9812465.3192528.30.2244608.5558408.7803
420.000.0023390.00100257.757083.9122318.3882402.383.9142453.4862537.40.2964808.3695208.6660
525.000.0031700.00100343.3370104.8302304.2702409.1104.8302441.6702546.50.3672208.1893808.5566
630.000.0042470.00100432.8780125.7302290.1702415.9125.7302429.7702555.50.4367508.0152508.4520
735.000.0056290.00100625.2050146.6302276.0702422.7146.6302417.8702564.50.5051307.8465708.3517
840.000.0073850.00100819.5150167.5302261.8702429.4167.5302405.9702573.50.5724007.6831008.2555
945.000.0095950.00101015.2520188.4302247.6702436.1188.4302393.9702582.40.6386107.5246908.1633
1050.000.0123520.00101212.0270209.3302233.3702442.7209.3402381.9602591.30.7038107.3709908.0748
1155.000.0157620.0010159.5643230.2402219.0602449.3230.2602369.8402600.10.7680207.2217807.9898
1260.000.0199460.0010177.6672251.1602204.7402455.9251.1802357.6202608.80.8312907.0768107.9081
1365.000.0250420.0010206.1935272.0902190.3102462.4272.1202345.3802617.50.8936506.9359507.8296
1470.000.0312010.0010235.0395293.0302175.8702468.9293.0702333.0302626.10.9551306.7988707.7540
1575.000.0385950.0010264.1289313.9902161.2102475.2314.0302320.5702634.61.0158006.6654007.6812
1680.000.0474140.0010293.4052334.9602146.6402481.6335.0102307.9902643.01.0756006.5355007.6111
1785.000.0578670.0010322.8258355.9502131.8502487.8356.0102295.2902651.31.1346006.4088007.5434
1890.000.0701820.0010362.3591376.9702117.0302494.0377.0402282.4602659.51.1929006.2852007.4781
1995.000.0846080.0010401.9806398.0002102.0002500.0398.0902269.5102667.61.2504006.1647007.4151
\n", "
" ], "text/plain": [ " Temperature (C) Pressure (MPa) Volume (l, m3/kg) Volume (v, m3/kg) \\\n", "0 0.01 0.000612 0.001000 205.9900 \n", "1 5.00 0.000873 0.001000 147.0100 \n", "2 10.00 0.001228 0.001000 106.3000 \n", "3 15.00 0.001706 0.001001 77.8750 \n", "4 20.00 0.002339 0.001002 57.7570 \n", "5 25.00 0.003170 0.001003 43.3370 \n", "6 30.00 0.004247 0.001004 32.8780 \n", "7 35.00 0.005629 0.001006 25.2050 \n", "8 40.00 0.007385 0.001008 19.5150 \n", "9 45.00 0.009595 0.001010 15.2520 \n", "10 50.00 0.012352 0.001012 12.0270 \n", "11 55.00 0.015762 0.001015 9.5643 \n", "12 60.00 0.019946 0.001017 7.6672 \n", "13 65.00 0.025042 0.001020 6.1935 \n", "14 70.00 0.031201 0.001023 5.0395 \n", "15 75.00 0.038595 0.001026 4.1289 \n", "16 80.00 0.047414 0.001029 3.4052 \n", "17 85.00 0.057867 0.001032 2.8258 \n", "18 90.00 0.070182 0.001036 2.3591 \n", "19 95.00 0.084608 0.001040 1.9806 \n", "\n", " Internal Energy (l, kJ/kg) Δ Internal Energy of Vapourization (kJ/kg) \\\n", "0 0.000 2374.900 \n", "1 21.019 2360.781 \n", "2 42.020 2346.580 \n", "3 62.980 2332.520 \n", "4 83.912 2318.388 \n", "5 104.830 2304.270 \n", "6 125.730 2290.170 \n", "7 146.630 2276.070 \n", "8 167.530 2261.870 \n", "9 188.430 2247.670 \n", "10 209.330 2233.370 \n", "11 230.240 2219.060 \n", "12 251.160 2204.740 \n", "13 272.090 2190.310 \n", "14 293.030 2175.870 \n", "15 313.990 2161.210 \n", "16 334.960 2146.640 \n", "17 355.950 2131.850 \n", "18 376.970 2117.030 \n", "19 398.000 2102.000 \n", "\n", " Internal Energy (v, kJ/kg) Enthalpy (l, kJ/kg) \\\n", "0 2374.9 0.000 \n", "1 2381.8 21.020 \n", "2 2388.6 42.021 \n", "3 2395.5 62.981 \n", "4 2402.3 83.914 \n", "5 2409.1 104.830 \n", "6 2415.9 125.730 \n", "7 2422.7 146.630 \n", "8 2429.4 167.530 \n", "9 2436.1 188.430 \n", "10 2442.7 209.340 \n", "11 2449.3 230.260 \n", "12 2455.9 251.180 \n", "13 2462.4 272.120 \n", "14 2468.9 293.070 \n", "15 2475.2 314.030 \n", "16 2481.6 335.010 \n", "17 2487.8 356.010 \n", "18 2494.0 377.040 \n", "19 2500.0 398.090 \n", "\n", " Δ Enthalpy of Vapourization (kJ/kg) Enthalpy (v, kJ/kg) \\\n", "0 2500.900 2500.9 \n", "1 2489.080 2510.1 \n", "2 2477.179 2519.2 \n", "3 2465.319 2528.3 \n", "4 2453.486 2537.4 \n", "5 2441.670 2546.5 \n", "6 2429.770 2555.5 \n", "7 2417.870 2564.5 \n", "8 2405.970 2573.5 \n", "9 2393.970 2582.4 \n", "10 2381.960 2591.3 \n", "11 2369.840 2600.1 \n", "12 2357.620 2608.8 \n", "13 2345.380 2617.5 \n", "14 2333.030 2626.1 \n", "15 2320.570 2634.6 \n", "16 2307.990 2643.0 \n", "17 2295.290 2651.3 \n", "18 2282.460 2659.5 \n", "19 2269.510 2667.6 \n", "\n", " Entropy (l, J/g*K) Δ Entropy of Vapourization (kJ/kg) Entropy (v, J/g*K) \n", "0 0.000000 9.155500 9.1555 \n", "1 0.076254 8.948546 9.0248 \n", "2 0.151090 8.748710 8.8998 \n", "3 0.224460 8.555840 8.7803 \n", "4 0.296480 8.369520 8.6660 \n", "5 0.367220 8.189380 8.5566 \n", "6 0.436750 8.015250 8.4520 \n", "7 0.505130 7.846570 8.3517 \n", "8 0.572400 7.683100 8.2555 \n", "9 0.638610 7.524690 8.1633 \n", "10 0.703810 7.370990 8.0748 \n", "11 0.768020 7.221780 7.9898 \n", "12 0.831290 7.076810 7.9081 \n", "13 0.893650 6.935950 7.8296 \n", "14 0.955130 6.798870 7.7540 \n", "15 1.015800 6.665400 7.6812 \n", "16 1.075600 6.535500 7.6111 \n", "17 1.134600 6.408800 7.5434 \n", "18 1.192900 6.285200 7.4781 \n", "19 1.250400 6.164700 7.4151 " ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "df = pd.read_excel('../figures/Module-4/SatTandPofSteam.xlsx', sheet_name='Sheet2', index_col=None, na_values=['NA'])\n", "df.head(20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another type of table is a super heated steam table at a given pressure. Here is an example of this type table." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Temperature (C)Pressure (MPa)Volume (m3/kg)Internal Energy (kJ/kg)Enthalpy (kJ/kg)Entropy (J/g*K)
0233.8530.0666642603.22803.26.1856
1250.0030.0706272644.72856.56.2893
2300.0030.0811792750.82994.36.5412
3350.0030.0905562844.43116.16.7449
4400.0030.0993792933.53231.76.9234
5450.0030.1078903021.23344.87.0856
6500.0030.1162003108.63457.27.2359
7550.0030.1243703196.63569.77.3768
8600.0030.1324503285.53682.87.5103
9650.0030.1404503375.63796.97.6373
10700.0030.1484103467.03912.27.7590
11750.0030.1563203559.94028.97.8758
12800.0030.1642003654.34146.97.9885
13850.0030.1720503750.34266.58.0973
14900.0030.1798803847.94387.58.2028
15950.0030.1876903947.04510.18.3051
161000.0030.1954904047.74634.18.4045
\n", "
" ], "text/plain": [ " Temperature (C) Pressure (MPa) Volume (m3/kg) Internal Energy (kJ/kg) \\\n", "0 233.85 3 0.066664 2603.2 \n", "1 250.00 3 0.070627 2644.7 \n", "2 300.00 3 0.081179 2750.8 \n", "3 350.00 3 0.090556 2844.4 \n", "4 400.00 3 0.099379 2933.5 \n", "5 450.00 3 0.107890 3021.2 \n", "6 500.00 3 0.116200 3108.6 \n", "7 550.00 3 0.124370 3196.6 \n", "8 600.00 3 0.132450 3285.5 \n", "9 650.00 3 0.140450 3375.6 \n", "10 700.00 3 0.148410 3467.0 \n", "11 750.00 3 0.156320 3559.9 \n", "12 800.00 3 0.164200 3654.3 \n", "13 850.00 3 0.172050 3750.3 \n", "14 900.00 3 0.179880 3847.9 \n", "15 950.00 3 0.187690 3947.0 \n", "16 1000.00 3 0.195490 4047.7 \n", "\n", " Enthalpy (kJ/kg) Entropy (J/g*K) \n", "0 2803.2 6.1856 \n", "1 2856.5 6.2893 \n", "2 2994.3 6.5412 \n", "3 3116.1 6.7449 \n", "4 3231.7 6.9234 \n", "5 3344.8 7.0856 \n", "6 3457.2 7.2359 \n", "7 3569.7 7.3768 \n", "8 3682.8 7.5103 \n", "9 3796.9 7.6373 \n", "10 3912.2 7.7590 \n", "11 4028.9 7.8758 \n", "12 4146.9 7.9885 \n", "13 4266.5 8.0973 \n", "14 4387.5 8.2028 \n", "15 4510.1 8.3051 \n", "16 4634.1 8.4045 " ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "df = pd.read_excel('../figures/Module-4/Steam_3MPa.xlsx', sheet_name='Sheet2', index_col=None, na_values=['NA'])\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "## 4.6.3 – How to Use Steam Tables\n", "\n", "Steam tables are typically used to calculate the change in energy in a specific process, whether it be energy generation or cooling. By measuring the changes in pressure or temperature of steam, you can calculate changes in enthalpy or internal energy. For example, if you have 1 kg of steam at $800.00 ^{\\circ} C$ and 3.0000 MPa and you cool it to $600.00 ^{\\circ} C$ at a constant pressure you change in enthalpy $\\Delta H = H_2 - H_1 =(3682.8 - 4146.9) \\space kJ/kg = -464.1 \\space kJ/kg$. \n", "\n", "Be aware of keywords such as superheated steam, superheated liquid, and saturated steam.\n", "__Saturated steam__ is the least amount of heat required to bring water to steam at a certain pressure. Concurrently, there will be a set temperature associated with it as well. __Superheated steam__ is saturated steam that has much more heat added, raising the temperature and enthalpy considerably. __Superheated liquid__ is water under high pressure being heated. \n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.6.4 – Interpolation\n", "\n", "Let's suppose you wanted to find out what the internal energy of steam is at $725.00 ^{\\circ} C$ and $3.0000 \\space \\text{MPa}$. Since the value is not given in the table, you must interpolate. The formula for interpolation is: \n", "\n", "$$ y = \\frac{y_2 - y_1}{x_2 - x_1} (x - x_1) + y_1 $$\n", "\n", "In this case the formula for internal energy at $725.00 ^{\\circ} C$ is:\n", "\n", "$$ U_{3 MPa, 725 C} = \\frac{U_{3 MPa, 750 C} - U_{3 MPa, 700 C}}{T_2 - T_1} (T - T_1) + U_{3 MPa, 700 C} $$\n", "\n", "and the answer is:\n", "\n", "$$ U_{3 MPa, 725 C} = \\frac{(3559.9 - 3467.0 ) \\space kJ/kg}{(750 - 700) \\space C} (725 - 700) \\space C + 3467.0 \\space kJ/kg = 3513.45 \\space kJ/kg $$\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4.6.5 – Problem Statement\n", "\n", "### Question\n", "Using the steam tables below, find the change in internal energy when steam is first cooled isobarically at $750.00 ^{\\circ} C$ and $5.0000 \\space \\text{MPa}$ to $725.00 ^{\\circ} C \\space$ and $5.0000 \\space \\text{MPa}$ and then expanded isothermally at $725.00 ^{\\circ} C$ from $5.0000 \\space \\text{MPa}$ to $1.0000 \\space \\text{MPa}$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Temperature (C)Pressure (MPa)Volume (m3/kg)Internal Energy (kJ/kg)Enthalpy (kJ/kg)Entropy (J/g*K)
0263.9450.0394462597.02794.25.9737
1300.0050.0453462699.02925.76.2110
2350.0050.0519692809.53069.36.4516
3400.0050.0578372907.53196.76.6483
4450.0050.0633233000.63317.26.8210
5500.0050.0685833091.73434.76.9781
6550.0050.0736943182.43550.97.1237
7600.0050.0787043273.33666.87.2605
8650.0050.0836393365.03783.27.3901
9700.0050.0885183457.73900.37.5136
10750.0050.0933553551.64018.47.6320
11800.0050.0981583646.94137.77.7458
12850.0050.1029303743.64258.37.8556
13900.0050.1076903841.84380.27.9618
14950.0050.1124203941.54503.68.0648
151000.0050.1171504042.64628.38.1648
\n", "
" ], "text/plain": [ " Temperature (C) Pressure (MPa) Volume (m3/kg) Internal Energy (kJ/kg) \\\n", "0 263.94 5 0.039446 2597.0 \n", "1 300.00 5 0.045346 2699.0 \n", "2 350.00 5 0.051969 2809.5 \n", "3 400.00 5 0.057837 2907.5 \n", "4 450.00 5 0.063323 3000.6 \n", "5 500.00 5 0.068583 3091.7 \n", "6 550.00 5 0.073694 3182.4 \n", "7 600.00 5 0.078704 3273.3 \n", "8 650.00 5 0.083639 3365.0 \n", "9 700.00 5 0.088518 3457.7 \n", "10 750.00 5 0.093355 3551.6 \n", "11 800.00 5 0.098158 3646.9 \n", "12 850.00 5 0.102930 3743.6 \n", "13 900.00 5 0.107690 3841.8 \n", "14 950.00 5 0.112420 3941.5 \n", "15 1000.00 5 0.117150 4042.6 \n", "\n", " Enthalpy (kJ/kg) Entropy (J/g*K) \n", "0 2794.2 5.9737 \n", "1 2925.7 6.2110 \n", "2 3069.3 6.4516 \n", "3 3196.7 6.6483 \n", "4 3317.2 6.8210 \n", "5 3434.7 6.9781 \n", "6 3550.9 7.1237 \n", "7 3666.8 7.2605 \n", "8 3783.2 7.3901 \n", "9 3900.3 7.5136 \n", "10 4018.4 7.6320 \n", "11 4137.7 7.7458 \n", "12 4258.3 7.8556 \n", "13 4380.2 7.9618 \n", "14 4503.6 8.0648 \n", "15 4628.3 8.1648 " ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "df = pd.read_excel('../figures/Module-4/Steam_5MPa.xlsx', sheet_name='Sheet2', index_col=None, na_values=['NA'])\n", "df" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Temperature (C)Pressure (MPa)Volume (m3/kg)Internal Energy (kJ/kg)Enthalpy (kJ/kg)Entropy (J/g*K)
0179.8810.194362582.72777.16.5850
1200.0010.206022622.22828.36.6955
2250.0010.232752710.42943.16.9265
3300.0010.257992793.63051.67.1246
4350.0010.282502875.73158.27.3029
5400.0010.306612957.93264.57.4669
6450.0010.330453040.93371.37.6200
7500.0010.354113125.03479.17.7641
8550.0010.377663210.53588.17.9008
9600.0010.401113297.53698.68.0310
10650.0010.424493386.03810.58.1557
11700.0010.447833476.23924.18.2755
12750.0010.471123568.14039.38.3909
13800.0010.494383661.74156.18.5024
14850.0010.517623757.04274.68.6103
15900.0010.540833853.94394.88.7150
16950.0010.564033952.54516.58.8166
171000.0010.587214052.74639.98.9155
\n", "
" ], "text/plain": [ " Temperature (C) Pressure (MPa) Volume (m3/kg) Internal Energy (kJ/kg) \\\n", "0 179.88 1 0.19436 2582.7 \n", "1 200.00 1 0.20602 2622.2 \n", "2 250.00 1 0.23275 2710.4 \n", "3 300.00 1 0.25799 2793.6 \n", "4 350.00 1 0.28250 2875.7 \n", "5 400.00 1 0.30661 2957.9 \n", "6 450.00 1 0.33045 3040.9 \n", "7 500.00 1 0.35411 3125.0 \n", "8 550.00 1 0.37766 3210.5 \n", "9 600.00 1 0.40111 3297.5 \n", "10 650.00 1 0.42449 3386.0 \n", "11 700.00 1 0.44783 3476.2 \n", "12 750.00 1 0.47112 3568.1 \n", "13 800.00 1 0.49438 3661.7 \n", "14 850.00 1 0.51762 3757.0 \n", "15 900.00 1 0.54083 3853.9 \n", "16 950.00 1 0.56403 3952.5 \n", "17 1000.00 1 0.58721 4052.7 \n", "\n", " Enthalpy (kJ/kg) Entropy (J/g*K) \n", "0 2777.1 6.5850 \n", "1 2828.3 6.6955 \n", "2 2943.1 6.9265 \n", "3 3051.6 7.1246 \n", "4 3158.2 7.3029 \n", "5 3264.5 7.4669 \n", "6 3371.3 7.6200 \n", "7 3479.1 7.7641 \n", "8 3588.1 7.9008 \n", "9 3698.6 8.0310 \n", "10 3810.5 8.1557 \n", "11 3924.1 8.2755 \n", "12 4039.3 8.3909 \n", "13 4156.1 8.5024 \n", "14 4274.6 8.6103 \n", "15 4394.8 8.7150 \n", "16 4516.5 8.8166 \n", "17 4639.9 8.9155 " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "df = pd.read_excel('../figures/Module-4/Steam_1MPa.xlsx', sheet_name='Sheet2', index_col=None, na_values=['NA'])\n", "df" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Answer\n", "\n", "The internal energy at $750.00 ^{\\circ} C$ and $5.0000 \\space \\text{MPa}$ is\n", "\n", "$$ U_{5 MPa, 750 C} = 3511.6 \\space kJ/kg $$\n", "\n", "Since $725.00 ^{\\circ} C$ is not present in the first table, we must interpolate\n", "\n", "$$ U_{5 MPa, 725 C} = \\frac{U_{5 MPa, 750 C} - U_{5 MPa, 700 C}}{T_2 - T_1} (T - T_1) + U_{5 MPa, 700 C} $$\n", "\n", "$$ U_{5 MPa, 725 C} = \\frac{(3511.6 - 3457.7 ) \\space kJ/kg}{(750 - 700) \\space C} (725 - 700) \\space C + 3457.7 \\space kJ/kg $$\n", "\n", "$$ U_{5 MPa, 725 C} = 3,484.65 \\space kJ/kg $$\n", "\n", "now that we have $U_{5 MPa, 725 C}$, we must find $U_{1 MPa, 725 C}$ using interpolation\n", "\n", "$$ U_{1 MPa, 725 C} = \\frac{U_{1 MPa, 750 C} - U_{1 MPa, 700 C}}{T_2 - T_1} (T - T_1) + U_{1 MPa, 700 C} $$\n", "\n", "$$ U_{1 MPa, 725 C} = \\frac{(3568.1 - 3476.2 ) \\space kJ/kg}{(750 - 700) \\space C} (725 - 700) \\space C + 3476.2 \\space kJ/kg $$\n", "\n", "$$ U_{1 MPa, 725 C} = 3,522.15 \\space kJ/kg $$\n", "\n", "Now that we have all the necessary values, we just need to sum the changes in internal energy\n", "\n", "$$ \\Delta U_{tot} = \\Delta U_{1} + \\Delta U_{2} = (U_{5 MPa, 725 C} - U_{5 MPa, 750 C}) + (U_{1 MPa, 725 C} - U_{5 MPa, 725 C}) $$\n", "\n", "$$ \\Delta U_{tot} = (3,484.65 \\space kJ/kg - \t3551.6 \\space kJ/kg) + (3,522.15 \\space kJ/kg - 3,484.65 \\space kJ/kg) $$\n", "\n", "$$ \\Delta U_{tot} = -10.6 \\space kJ/kg $$" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }