{"id":1497,"date":"2025-12-07T08:03:51","date_gmt":"2025-12-07T07:03:51","guid":{"rendered":"https:\/\/control-advent.com\/?p=1497"},"modified":"2025-12-07T08:03:53","modified_gmt":"2025-12-07T07:03:53","slug":"07-two-candles-for-the-perfect-cup-of-punch","status":"publish","type":"post","link":"https:\/\/control-advent.com\/?p=1497","title":{"rendered":"07 &#8211; Two candles for the perfect cup of punch?"},"content":{"rendered":"\n<p>Elf Elfis is in charge of keeping a pot of warm punch cozy for the elves\u2019 winter party. The punch is heated by placing candles under the pot.<\/p>\n\n\n\n<p>He knows that when the room temperature is 22\u202f\u00b0C and he places one candle under the pot, the punch reaches 32\u202f\u00b0C. Elf Merry-Linn explained that the punch loses heat to the room at a rate proportional to the square of the difference between the punch temperature and the room temperature.<\/p>\n\n\n\n<p>Curious to see the effect of more heat, Elfis decides to place two candles under the pot.<\/p>\n\n\n\n<p>What will the temperature of the punch then approximately be with two candles under it?<\/p>\n\n\n\n<p>a. \ud83c\udf21\ufe0f\ud83e\udd44\u2744\ufe0f 31\u202f\u00b0C<\/p>\n\n\n\n<p>b. \ud83d\udd25\u2615\u2728 32\u202f\u00b0C<\/p>\n\n\n\n<p>c. \ud83d\udd6f\ufe0f\u2603\ufe0f\ud83c\udf89 33\u202f\u00b0C<\/p>\n\n\n\n<p>d. \u2615\ud83c\udf84\u2744\ufe0f 34\u202f\u00b0C<\/p>\n\n\n\n<p>e. \ud83c\udf81\ud83d\udd6f\ufe0f\u2728 35\u202f\u00b0C<\/p>\n\n\n\n<p>f. \u2744\ufe0f\ud83d\udd25\u2615 36\u202f\u00b0C<\/p>\n\n\n\n<p>g. \ud83e\udd73\u2603\ufe0f\ud83d\udd6f\ufe0f 37\u202f\u00b0C<\/p>\n\n\n\n<p>h. \ud83c\udf1f\u2615\ud83c\udf81 38\u202f\u00b0C<\/p>\n\n\n\n<p>i. \ud83d\udd6f\ufe0f\ud83c\udf89\u2744\ufe0f 39\u202f\u00b0C<\/p>\n\n\n\n<p>j. \u2615\ud83d\udd25\ud83c\udf1f 40\u202f\u00b0C<\/p>\n\n\n<div class='bootstrap-yop yop-poll-mc'>\n\t\t\t\t\t\t\t<div class=\"basic-yop-poll-container\" style=\"background-color:#b70004; border:0px; border-style:solid; border-color:#b70004; border-radius:0px; padding:10px 10px;\" data-id=\"44\" data-temp=\"basic\" data-skin=\"minimal\" data-cscheme=\"black\" data-cap=\"0\" data-access=\"wordpress\" data-tid=\"\" data-uid=\"f216440f3c7f58447e0f10c2ad679842\" data-pid=\"1497\" data-resdet=\"percentages\" data-show-results-to=\"\" data-show-results-moment=\"never\" data-show-results-only=\"false\" data-show-message=\"true\" data-show-results-as=\"bar\" data-sort-results-by=\"as-defined\" data-sort-results-rule=\"asc\"data-is-ended=\"0\" data-gdpr=\"no\" data-gdpr-sol=\"consent\" data-css=\".basic-yop-poll-container[data-uid] .basic-vote { text-align: center; }\" data-counter=\"0\" data-load-with=\"1\" data-notification-section=\"top\"><div class=\"row\"><div class=\"col-md-12\"><div class=\"basic-inner\"><div class=\"basic-message hide\" style=\"border-left: 10px solid #008000; padding: 0px 10px;\" data-error=\"#ff0000\" data-success=\"#008000\"><p class=\"basic-message-text\" style=\"color:#000000; font-size:14px; font-weight:normal;\"><\/p><\/div><div class=\"basic-overlay hide\"><div class=\"basic-vote-options\"><\/div><div class=\"basic-preloader\"><div class=\"basic-windows8\"><div class=\"basic-wBall basic-wBall_1\"><div class=\"basic-wInnerBall\"><\/div><\/div><div class=\"basic-wBall basic-wBall_2\"><div class=\"basic-wInnerBall\"><\/div><\/div><div class=\"basic-wBall basic-wBall_3\"><div class=\"basic-wInnerBall\"><\/div><\/div><div class=\"basic-wBall basic-wBall_4\"><div class=\"basic-wInnerBall\"><\/div><\/div><div class=\"basic-wBall basic-wBall_5\"><div class=\"basic-wInnerBall\"><\/div><\/div><\/div><\/div><\/div><form class=\"basic-form\"><input type=\"hidden\" name=\"_token\" value=\"a6a7503830\" autocomplete=\"off\"><div class=\"basic-elements\"><div class=\"basic-element basic-question basic-question-text-horizontal\" data-id=\"44\" data-uid=\"3c5d5fe2d716bfdce8430a3f8cc2f6f3\" data-type=\"question\" data-question-type=\"text\" data-allow-multiple=\"no\" data-min=\"1\" data-max=\"1\" data-display=\"horizontal\" data-colnum=\"\" data-display-others=\"no\" data-others-color=\"\" data-others=\"\"><div role=\"heading\" aria-level=\"5\" class=\"basic-question-title\" style=\"color:#ffffff; font-size:14px; font-weight:normal; text-align:center;\">Choose an option:<\/div><ul class=\"basic-answers basic-h-answers\"><li class=\"basic-answer col-xs-6 col-sm-6 cols-10\" style=\"padding:0px 0px;\" data-id=\"367\" data-type=\"text\" data-vn=\"0\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[367]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[367]\" name=\"answer[44]\" value=\"367\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">a<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 cols-10\" style=\"padding:0px 0px;\" data-id=\"368\" data-type=\"text\" data-vn=\"0\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[368]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[368]\" name=\"answer[44]\" value=\"368\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">b<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 cols-10\" style=\"padding:0px 0px;\" data-id=\"369\" data-type=\"text\" data-vn=\"1\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[369]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[369]\" name=\"answer[44]\" value=\"369\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">c<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 cols-10\" style=\"padding:0px 0px;\" data-id=\"373\" data-type=\"text\" data-vn=\"0\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[373]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[373]\" name=\"answer[44]\" value=\"373\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">d<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 cols-10\" style=\"padding:0px 0px;\" data-id=\"374\" data-type=\"text\" data-vn=\"1\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[374]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[374]\" name=\"answer[44]\" value=\"374\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">e<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 cols-10\" style=\"padding:0px 0px;\" data-id=\"376\" data-type=\"text\" data-vn=\"46\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[376]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[376]\" name=\"answer[44]\" value=\"376\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">f<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 cols-10\" style=\"padding:0px 0px;\" data-id=\"377\" data-type=\"text\" data-vn=\"0\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[377]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[377]\" name=\"answer[44]\" value=\"377\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">g<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 cols-10\" style=\"padding:0px 0px;\" data-id=\"378\" data-type=\"text\" data-vn=\"1\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[378]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[378]\" name=\"answer[44]\" value=\"378\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">h<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 cols-10\" style=\"padding:0px 0px;\" data-id=\"379\" data-type=\"text\" data-vn=\"1\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[379]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[379]\" name=\"answer[44]\" value=\"379\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">i<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 cols-10\" style=\"padding:0px 0px;\" data-id=\"380\" data-type=\"text\" data-vn=\"0\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[380]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[380]\" name=\"answer[44]\" value=\"380\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">j<\/span><\/label><\/div><\/li><\/ul><\/div><div class=\"clearfix\"><\/div><\/div><div class=\"basic-vote\"><a href=\"#\" class=\"button basic-vote-button\" role=\"button\" style=\"background:#ffffff; border:1px; border-style: solid; border-color:#000000; border-radius:0px; padding:5px 10px; color:#000000; font-size:14px; font-weight:normal;\">&gt;&gt;&gt;<\/a><\/div><\/form><div class=\"yop-poll-modal\"><div class=\"yop-poll-modal-content\"><div class=\"yop-poll-modal-header\"><span class=\"yop-poll-modal-close\">&times;<\/span><\/div><div class=\"yop-poll-modal-body\"><div class=\"yop-poll-form-group\"><label class=\"yop-poll-user-or-email-label\">Username or Email Address<\/label><input type=\"text\" class=\"yop-poll-user-or-email-input\" autocomplete=\"off\"><\/div><div class=\"yop-poll-form-group\"><label class=\"yop-poll-password-label\">Password<\/label><input type=\"password\" class=\"yop-poll-password-input\" autocomplete=\"off\"><\/div><div class=\"yop-poll-form-group submit\"><button class=\"button button-primary button-large yop-poll-login-button\">Log In<\/button><\/div><div class=\"yop-poll-form-group yop-poll-section-login-options\"><p><a href=\"https:\/\/control-advent.com\/wp-login.php?action=register\" target=\"_blank\">No account? Register here<\/a><\/p><p><a href=\"https:\/\/control-advent.com\/wp-login.php?action=lostpassword\" target=\"_blank\">Forgot password<\/a><\/p><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>\n\t\t\t\t\t\t<\/div>\n\n\n\n<p><strong>Related control topic: steady state value<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Elf Elfis is in charge of keeping a pot of warm punch cozy for the elves\u2019 winter party. The punch is heated by placing candles under the pot. He knows that when the room temperature is 22\u202f\u00b0C and he places &hellip; <span class=\"more-link\"><a href=\"https:\/\/control-advent.com\/?p=1497\" class=\"readmore\">Continue reading<span class=\"screen-reader-text\">07 &#8211; Two candles for the perfect cup of punch?<\/span><\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":1498,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[111],"class_list":["post-1497","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-english","tag-2025-en"],"_links":{"self":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1497","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1497"}],"version-history":[{"count":1,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1497\/revisions"}],"predecessor-version":[{"id":1499,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1497\/revisions\/1499"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/media\/1498"}],"wp:attachment":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1497"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1497"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1497"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}