{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"frontierscience","formal_name":"FrontierScience","introduction":"FrontierScience evaluates the ability to solve expert-level scientific tasks. Its public data separates olympiad and research problems so that competition and research tasks can be examined independently.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/openai/frontierscience","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"585e9848-0f29-5106-81d1-10f6a1b374ac","task_key":"olympiad--test--0ea11f5b~2ddf09~2d4330~2d92cc~2d302a63c22008","task_revision_id":"2","upstream_id":"0ea11f5b-df09-4330-92cc-302a63c22008","short_description":"For rising moist air of molar heat capacity `\\( c_p \\)`, molar latent heat `\\( L…","config":"olympiad","split":"test","body":"{\"problem\":\"For rising moist air of molar heat capacity `\\\\( c_p \\\\)`, molar latent heat `\\\\( L \\\\)`, molar mass `\\\\( M \\\\)`, the temperature fluctuates with height.\\n\\nYou can assume\\n`\\\\[ \\n\\\\frac{\\\\Delta T}{T} = \\\\frac{1 + \\\\alpha \\\\rho_s}{1 + \\\\beta \\\\rho_s \\\\gamma}\\\\frac{\\\\beta}{\\\\alpha}\\\\rho\\n \\\\]`\\nwhere `\\\\( \\\\alpha = L/(RT), \\\\beta = L/(c_pT), \\\\rho_s = P_s/P, \\\\rho = \\\\Delta P/P, \\\\)` and `\\\\( \\\\gamma = \\\\frac{TdP_s}{P_sdT} \\\\)`. Here, `\\\\( R,T,P,P_s,\\\\Delta \\\\)` are the universal gas constant, air temperature, air pressure, saturated vapour pressure of water (where `\\\\( P_s  \\\\)` is a monotonic function of `\\\\(T\\\\)`) and the small fluctuation operator respectively.\\n\\nThe Clausius-Clapeyron relation states: `\\\\( \\\\frac{dP_s}{dT} = \\\\frac{L}{T(v_1 - v_2)} \\\\)`, where `\\\\( v_1 \\\\)` and `\\\\( v_2 \\\\)` are the molar volumes of water vapor and liquid water, respectively (with `\\\\( v_2 \\\\ll v_1 \\\\)` ).\\n\\nDerive an equation for the Temperature Lapse Rate `\\\\( \\\\Delta T/\\\\Delta h \\\\)` in terms of `\\\\( M, g, R, P, \\\\alpha , \\\\beta \\\\)` and `\\\\( \\\\rho_s  \\\\)`.\\n\\nThink step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.\",\"subject\":\"physics\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/openai/frontierscience","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}