{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"mmlu-pro","formal_name":"MMLU-Pro","introduction":"MMLU-Pro rebuilds MMLU with ten answer options instead of four and removes items that no longer separate models. Questions span fourteen academic and professional subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/TIGER-Lab/MMLU-Pro","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"acccdf85-1a8c-5498-8121-ca2d81ab995a","task_key":"default--test--11707","task_revision_id":"1","upstream_id":"11707","short_description":"200 Kg of water at T_i = 35°C is kept in an auxiliary reservoir tobe heated by…","config":"default","split":"test","body":"{\"category\":\"engineering\",\"options\":\"['55%', '50%', '42%', '30%', '35%', '40%', '22.2%', '18.7%', '33.3%', '27.5%']\",\"question\":\"200 Kg of water at T_i = 35°C is kept in an auxiliary reservoir tobe heated by solar energy. The solar collector used has a surfacearea of A = 5m^2. The heat removal factor and the overallheat transfer coefficient are F_R = 0.80 and U_L = 8.0 W/m^2.°C, respectively. The ambient temperature T_a = 30°C. The product of the heat transfer coefficient and reservoirarea is (UA) = 1.80 W/°C. During an emergency, thewater will be used at a rate ṁ = 15 kg/hr and is refilled at atemperatureT_rf= 20°C. Determine the efficiency of this operationfrom 7 am to 5 pm. Refer to table 1 for hourly solar data. Table 1 I_T S T_a U_L(T_i - T_a) q = F_r S - U_L(T_i - T_a) \\\\eta = (q / I_T) Time MJ/m^2 MJ/m^2 °C MJ/m^2 MJ/m^2 7 - 8 0.03 - - 12 1.35 - - 8 - 9 0.49 0.40 - 9 1.27 0 0 9 - 10 1.12 0.92 - 3 1.09 0 0 10 - 11 4.02 3.26 3 1.01 1.80 0.45 11 - 12 3.45 3.08 4 0.89 1.75 0.51 12 - 1 4.15 3.39 7 0.81 2.20 0.53 1 - 2 3.96 3.20 8 0.78 1.94 0.49 2 - 3 1.98 1.58 9 0.75 0.67 0.34 3 - 4 1.27 1.01 10 0.72 0.23 0.18 4 - 5 0.04 - 8 0.78 - - \\\\sumI_T20.51 \\\\sum_q = 8.59 I_T - energy gained per hour by the solar panel. T_a - ambient temperature each hour. S - Incident heat flux on the solar panel. The overall efficiency is \\\\eta_day= [(\\\\sumq) / (\\\\sumI_T)] = [(8.59) / (20.42)] = 0.42 or 42% Table 2 I_T S T_a T_s^+ Q Loss Load Time MJ/m^2 MJ/m^2 °C °C MJ MJ MJ Begin 35.0 7 - 8 0.03 - - 12 33.2 0 0.021 0.83 8 - 9 0.49 0.40 - 9 31 .5 0 0.01 0.72 9 - 10 1.12 0.92 - 3 30.0 0 0 0.63 10 - 11 4.02 3.26 3 39.8 8.75 0.064 1.24 11 - 12 3.45 3.08 4 45.4 6.12 0.10 1.60 12 - 1 4.15 3.39 7 52.8 7.85 0.15 2.06 1 - 2 3.96 3.20 8 57.9 5.42 0.18 2.38 2 - 3 1.98 1.58 9 54.3 0 0.16 2.15 3 - 4 1.27 1.01 10 51 .6 0 0.14 1.98 4 - 5 0.04 - 8 48.6 0 0.12 1.80 \\\\sumI_T \\\\sumQ Losses \\\\sumLoads = 20.51 = 28.14 = 0.945 = 15.39\",\"src\":\"stemez-HeatTransfer\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/TIGER-Lab/MMLU-Pro","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}