// Numbas version: exam_results_page_options {"name": "A2: Ideal kinetic gas law", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "advice": "", "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"N": {"group": "Random Variables", "definition": "random(1.1..9.9#0.1 except 1)", "name": "N", "description": "", "templateType": "anything"}, "advice3": {"group": "Strings", "definition": "if(\n switcharoo<>4,\n \"$<v^2> = \\\\bigg(\\\\sqrt\\{<v^2>\\}\\\\bigg)^2 = \\\\big( \"+rms_vel+\" \\\\big)^2$ = \"+ms_vel,\" \"\n)", "name": "advice3", "description": "", "templateType": "anything"}, "answer_text": {"group": "Ungrouped variables", "definition": "switch(\n switcharoo=0,\n \" pressure of \"+sigformat(answer,3)+\" \"+if(m_l_switch=0,\" Pa\",\" atm\")\n ,switcharoo=1,\n \" volume is \"+sigformat(answer,3)+if(m_l_switch=0,\" m3\",\" L\")\n ,switcharoo=2,\n \"re are \"+sigformat(answer,3)+\" [x 1023] molecules\"\n ,switcharoo=3,\n \" mass of each molecule is \"+sigformat(answer,3)+\" [x 10-23] kg\"\n ,switcharoo=4,\n \" root-mean-squared velocity of molecules in the gas is \"+sigformat(answer,3)+\" m/s\"\n)", "name": "answer_text", "description": "", "templateType": "anything"}, "ms_vel": {"group": "Random Variables", "definition": "rms_vel^2", "name": "ms_vel", "description": "", "templateType": "anything"}, "V": {"group": "Random Variables", "definition": "random(0.1..3.0#0.1 except 1)", "name": "V", "description": "", "templateType": "anything"}, "p_string": {"group": "Strings", "definition": "if(switcharoo<>0,\" with a pressure of \"+if(m_l_switch=0,dpformat(p/1000,0)+\" kPa\",dpformat(p,2)+\" atm\"),\"\")", "name": "p_string", "description": "", "templateType": "anything"}, "explanation": {"group": "Answer Values", "definition": "\"so here, we calculate each of the five values based on the other four random versions, and then we can randomly decide which of the five is used for the question\"", "name": "explanation", "description": "", "templateType": "anything"}, "m": {"group": "Random Variables", "definition": "random(1.1..9.9)", "name": "m", "description": "", "templateType": "anything"}, "p": {"group": "Random Variables", "definition": "if(m_l_switch=0,random(10000..300000#10000),random(0.01..3.00#0.01 except 1))", "name": "p", "description": "", "templateType": "anything"}, "answer_txt2": {"group": "Ungrouped variables", "definition": "if(\n switcharoo=2,\n \"x 1023\"\n ,\n \"\"\n)+\nif(\n switcharoo=3,\n \"x 10-23\"\n ,\n \"\"\n)", "name": "answer_txt2", "description": "", "templateType": "anything"}, "VV": {"group": "Answer Values", "definition": "(1/3)*n23*m23*ms_vel/p", "name": "VV", "description": "", "templateType": "anything"}, "n23": {"group": "Random Variables", "definition": "n*10^23", "name": "n23", "description": "", "templateType": "anything"}, "a_string": {"group": "Strings", "definition": "switch(\n switcharoo=0,\n \"pressure of the gas in \"+if(m_l_switch=0,\"Pascals\",\" Atmospheres\")\n ,switcharoo=1,\n \"volume of the gas in \" +if(m_l_switch=0,\" cubic Meters\",\" Litres\")\n ,switcharoo=2,\n \"number of molecules in the gas, in units of [x 10$^\\{23\\}$] molecules,\"\n ,switcharoo=3,\n \"mass of each individual molecule, in units of [x 10$^\\{-23\\}$] kg,\"\n ,switcharoo=4,\n \"root-mean-square velocity (from the mean-square velocity in m/s) of the gas,\"\n)", "name": "a_string", "description": "", "templateType": "anything"}, "rms_vel": {"group": "Random Variables", "definition": "random(50..250)", "name": "rms_vel", "description": "", "templateType": "anything"}, "advice": {"group": "Strings", "definition": "\"$pV = 1/3 N m <v^2>$\"", "name": "advice", "description": "", "templateType": "anything"}, "mm23": {"group": "Answer Values", "definition": "3*p*V/(N23*ms_vel)", "name": "mm23", "description": "", "templateType": "anything"}, "T": {"group": "Random Variables", "definition": "random(100..800)", "name": "T", "description": "", "templateType": "anything"}, "nn": {"group": "Answer Values", "definition": "nn23/10^23", "name": "nn", "description": "

pV=1/3 Nm ms_vel

\n

N = 3pV/(m*ms_vel)

", "templateType": "anything"}, "kb": {"group": "Answer Values", "definition": "1", "name": "kb", "description": "", "templateType": "anything"}, "rrmmssvv": {"group": "Answer Values", "definition": "sqrt(mmssvv)", "name": "rrmmssvv", "description": "", "templateType": "anything"}, "advice_latex": {"group": "Strings", "definition": "switch(\n switcharoo=0,\n \"$p = \\\\frac\\{N m <v^2>\\}\\{3 V\\}$\"\n ,switcharoo=1,\n \"$V = \\\\frac\\{N m <v^2>\\}\\{3 p\\}$\"\n ,switcharoo=2,\n \"$N = \\\\frac\\{3 p V\\}\\{m <v^2>\\}$\"\n ,switcharoo=3,\n \"$m = \\\\frac\\{3 p V\\}\\{N <v^2>\\}$\"\n ,switcharoo=4,\n \"$T = \\\\frac\\{3 p V\\}\\{N m\\}$\"\n)", "name": "advice_latex", "description": "

switch(
switcharoo=0,\"p= 1/3 * N * m * &lt;v&gt;<sup>2</sup> / V\",
switcharoo=1,\"V = 1/3 * N * m * &lt;v&gt;<sup>2</sup> / p\",
switcharoo=2,\"N = 3 * p * V / (m * &lt;v&gt;<sup>2</sup>)\",
switcharoo=3,\"m = 3 * p * V / (N * &lt;v&gt;<sup>2</sup>)\",
switcharoo=4,\"&lt;v&gt;<sup>2</sup> = 3 * p * V / (N * m)\"
)

", "templateType": "anything"}, "k_c_switch": {"group": "Random Variables", "definition": "0", "name": "k_c_switch", "description": "", "templateType": "anything"}, "smv_string": {"group": "Strings", "definition": "if(switcharoo<>4,\"The root-mean-square velocity of the molecules in the gas is \"+rms_vel+\" m/s.\",\" \")", "name": "smv_string", "description": "", "templateType": "anything"}, "advice2": {"group": "Strings", "definition": "switch(\n switcharoo=0,\n \"$p = \\\\frac\\{\"+sigformat(N,3)+\"\\\\times10^\\{23\\} \\\\times \"+sigformat(m,3)+\"\\\\times10^\\{-23\\} \\\\times \"+sigformat(ms_vel,3)+\"\\}\\{3 * \"+sigformat(V,3)+\"\\}$\"\n ,switcharoo=1,\n \"$V = \\\\frac\\{\"+sigformat(N,3)+\"\\\\times10^\\{23\\} \\\\times \"+sigformat(m,3)+\"\\\\times10^\\{-23\\} \\\\times \"+sigformat(ms_vel,3)+\"\\}\\{3 * \"+sigformat(p,3)+\"\\}$\"\n ,switcharoo=2,\n \"$N = \\\\frac\\{3 \\\\times \"+sigformat(p,3)+\" \\\\times \"+sigformat(V,3)+\"\\}\\{\"+sigformat(m,3)+\"\\\\times10^\\{-23\\} \\\\times \"+sigformat(ms_vel,3)+\"\\}$\"\n ,switcharoo=3,\n \"$m = \\\\frac\\{3 \\\\times \"+sigformat(p,3)+\" \\\\times \"+sigformat(V,3)+\"\\}\\{\"+sigformat(N,3)+\"\\\\times10^\\{23\\} \\\\times \"+ms_vel+\"\\}$\"\n ,switcharoo=4,\n \"$<v^2> = \\\\frac\\{3 \\\\times \"+sigformat(p,3)+\" \\\\times \"+sigformat(V,3)+\"\\}\\{\"+sigformat(N,3)+\"\\\\times10^\\{23\\} \\\\times \"+sigformat(m,3)+\"\\\\times10^\\{-23\\}\\}$\"\n)", "name": "advice2", "description": "

switch(
switcharoo=0,\"p= 1/3 * N * m * &lt;v&gt;<sup>2</sup> / V\",
switcharoo=1,\"V = 1/3 * N * m * &lt;v&gt;<sup>2</sup> / p\",
switcharoo=2,\"N = 3 * p * V / (m * &lt;v&gt;<sup>2</sup>)\",
switcharoo=3,\"m = 3 * p * V / (N * &lt;v&gt;<sup>2</sup>)\",
switcharoo=4,\"&lt;v&gt;<sup>2</sup> = 3 * p * V / (N * m)\"
)

", "templateType": "anything"}, "m_l_switch": {"group": "Random Variables", "definition": "0", "name": "m_l_switch", "description": "", "templateType": "anything"}, "pp": {"group": "Answer Values", "definition": "(1/3)*n23*m23*ms_vel/V", "name": "pp", "description": "

pV=1/3 Nm ms_vel

\n

p

", "templateType": "anything"}, "answer2": {"group": "Ungrouped variables", "definition": "switch(\n switcharoo=0,pp,\n switcharoo=1,VV,\n switcharoo=2,nn,\n switcharoo=3,mm,\n switcharoo=4,mmssvv\n)", "name": "answer2", "description": "", "templateType": "anything"}, "nn23": {"group": "Answer Values", "definition": "3*p*V/(m23*ms_vel)", "name": "nn23", "description": "", "templateType": "anything"}, "m23": {"group": "Random Variables", "definition": "m*10^(-23)", "name": "m23", "description": "", "templateType": "anything"}, "m_string": {"group": "Strings", "definition": "if(switcharoo<>3,\"The mass of each molecule is \"+dpformat(m,2)+\" x 10-23 kg.\",\"\")", "name": "m_string", "description": "", "templateType": "anything"}, "n_string": {"group": "Strings", "definition": "if(switcharoo<>2,\"There are \"+dpformat(n,2)+\" x 1023 molecules in the gas.\",\"\")", "name": "n_string", "description": "", "templateType": "anything"}, "advice4": {"group": "Strings", "definition": "if(\n switcharoo=4, \n \"$\\\\sqrt\\{<v^2>\\} = \\\\sqrt\\{\"+sigformat(answer2,5)+\"}) =$\"+sigformat(answer,5),\" \"\n\n)", "name": "advice4", "description": "

", "templateType": "anything"}, "mmssvv": {"group": "Answer Values", "definition": "3*p*V/(m23*N23)", "name": "mmssvv", "description": "", "templateType": "anything"}, "v_string": {"group": "Strings", "definition": "if(switcharoo<>1,\"with a volume of \"+dpformat(v,2)+if(m_l_switch=0,\" m3\",\" L\"),\"\")", "name": "v_string", "description": "", "templateType": "anything"}, "mm": {"group": "Answer Values", "definition": "mm23*10^23", "name": "mm", "description": "", "templateType": "anything"}, "switcharoo": {"group": "Random Variables", "definition": "random(0..4)", "name": "switcharoo", "description": "", "templateType": "anything"}, "answer": {"group": "Ungrouped variables", "definition": "switch(\n switcharoo=0,pp,\n switcharoo=1,VV,\n switcharoo=2,nn,\n switcharoo=3,mm,\n switcharoo=4,rrmmssvv\n)", "name": "answer", "description": "", "templateType": "anything"}}, "name": "A2: Ideal kinetic gas law", "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

A simple ideal gas law question, using number of molecules, that asks the student to calculate one of the four variables. he question can ask for either L atm, or kPa m3, and either K or C for temp. As such the boltzmann constant is in either J/K or L atm/K.

\n

pV = 1/3 Nm<v2>

"}, "rulesets": {}, "extensions": [], "parts": [{"variableReplacementStrategy": "originalfirst", "precision": "3", "precisionPartialCredit": "50", "mustBeReduced": false, "maxValue": "siground(answer,3)+(siground(abs(answer),3)*0.01)", "precisionType": "sigfig", "scripts": {}, "customMarkingAlgorithm": "", "minValue": "siground(answer,3)-(siground(abs(answer),3)*0.01)", "type": "numberentry", "variableReplacements": [], "strictPrecision": true, "showPrecisionHint": false, "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "prompt": "

Calculate the {a_string} to three significant figures.