{"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 class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">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 class=\"wp-block-paragraph\">Curious to see the effect of more heat, Elfis decides to place two candles under the pot.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">What will the temperature of the punch then approximately be with two candles under it?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a. \ud83c\udf21\ufe0f\ud83e\udd44\u2744\ufe0f 31\u202f\u00b0C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b. \ud83d\udd25\u2615\u2728 32\u202f\u00b0C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c. \ud83d\udd6f\ufe0f\u2603\ufe0f\ud83c\udf89 33\u202f\u00b0C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d. \u2615\ud83c\udf84\u2744\ufe0f 34\u202f\u00b0C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">e. \ud83c\udf81\ud83d\udd6f\ufe0f\u2728 35\u202f\u00b0C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">f. \u2744\ufe0f\ud83d\udd25\u2615 36\u202f\u00b0C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">g. \ud83e\udd73\u2603\ufe0f\ud83d\udd6f\ufe0f 37\u202f\u00b0C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">h. \ud83c\udf1f\u2615\ud83c\udf81 38\u202f\u00b0C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">i. \ud83d\udd6f\ufe0f\ud83c\udf89\u2744\ufe0f 39\u202f\u00b0C<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">j. \u2615\ud83d\udd25\ud83c\udf1f 40\u202f\u00b0C<\/p>\n\n\n<div class=\"yop-poll yop-poll-container\" data-template=\"classic\" data-yop-poll-id=\"44\" data-yop-state=\"ballot\" data-yop-tracking=\"https:\/\/control-advent.com\" data-yop-page-id=\"0\" data-yop-msg-auth-failed=\"Sign-in failed. Please try again.\" data-yop-msg-no-provider=\"That sign-in method is unavailable.\" data-yop-msg-not-started=\"This poll is not accepting votes yet\" data-yop-msg-ended=\"This poll is no longer accepting votes\" data-yop-perm=\"wordpress\" style=\"background:#b70004;border-width:0px;border-style:none;border-color:#b70004;border-radius:0px;padding-top:10px;padding-bottom:10px;padding-left:10px;padding-right:10px;--yop-radio-color:black;--yop-ans-ts:14px;--yop-ans-tw:normal;--yop-ans-tc:#ffffff;--yop-ans-pt:0px;--yop-ans-pb:0px;--yop-ans-pl:0px;--yop-ans-pr:0px;--yop-poll-bg:#b70004;--yop-msg-bcs:#008000;--yop-msg-bce:#ff0000;--yop-msg-blw:10px;--yop-msg-pt:0px;--yop-msg-pb:0px;--yop-msg-pl:10px;--yop-msg-pr:10px;--yop-msg-tc:#000000;--yop-msg-ts:14px;--yop-msg-tw:normal;--yop-msg-br:0px;--yop-btn-bg:#ffffff;--yop-btn-tc:#000000;--yop-btn-bw:1px;--yop-btn-bs:solid;--yop-btn-bc:#000000;--yop-btn-br:0px;--yop-btn-pt:5px;--yop-btn-pb:5px;--yop-btn-pl:10px;--yop-btn-pr:10px;--yop-btn-ts:14px;--yop-btn-tw:normal;--yop-el-pt:10px;--yop-el-pb:10px;--yop-el-pl:0px;--yop-el-pr:0px;--yop-el-ta:center;--yop-q-tc:#ffffff;--yop-q-ts:14px;--yop-q-tw:normal\"><div class=\"yop-poll-decoy\" aria-hidden=\"true\"><input type=\"text\" name=\"website\" tabindex=\"-1\" autocomplete=\"off\" value=\"\" \/><\/div><div class=\"yop-poll-message\" data-yop-message role=\"status\" aria-live=\"polite\"><\/div><div class=\"yop-poll-ballot\" data-yop-page=\"0\"><div class=\"yop-poll-element\" data-element-type=\"question-text\" data-yop-el=\"44\" data-yop-required=\"1\" data-yop-msg-required=\"No answer selected\"><fieldset class=\"yop-poll-fieldset\"><legend id=\"yop-poll-44-44-label\" class=\"yop-poll-question\">Choose an option:<\/legend><div class=\"yop-poll-answers yop-poll-answers--horizontal\"><div class=\"yop-poll-answer-row\"><label class=\"yop-poll-answer\"><input type=\"radio\" name=\"yop-poll-44-44\" value=\"367\" data-yop-sub=\"367\" \/><span class=\"yop-poll-answer-text\"><span>a<\/span><\/span><\/label><\/div><div class=\"yop-poll-answer-row\"><label class=\"yop-poll-answer\"><input type=\"radio\" name=\"yop-poll-44-44\" value=\"368\" data-yop-sub=\"368\" \/><span class=\"yop-poll-answer-text\"><span>b<\/span><\/span><\/label><\/div><div class=\"yop-poll-answer-row\"><label class=\"yop-poll-answer\"><input type=\"radio\" name=\"yop-poll-44-44\" value=\"369\" data-yop-sub=\"369\" \/><span class=\"yop-poll-answer-text\"><span>c<\/span><\/span><\/label><\/div><div class=\"yop-poll-answer-row\"><label class=\"yop-poll-answer\"><input type=\"radio\" name=\"yop-poll-44-44\" value=\"373\" data-yop-sub=\"373\" \/><span class=\"yop-poll-answer-text\"><span>d<\/span><\/span><\/label><\/div><div class=\"yop-poll-answer-row\"><label class=\"yop-poll-answer\"><input type=\"radio\" name=\"yop-poll-44-44\" value=\"374\" data-yop-sub=\"374\" \/><span class=\"yop-poll-answer-text\"><span>e<\/span><\/span><\/label><\/div><div class=\"yop-poll-answer-row\"><label class=\"yop-poll-answer\"><input type=\"radio\" name=\"yop-poll-44-44\" value=\"376\" data-yop-sub=\"376\" \/><span class=\"yop-poll-answer-text\"><span>f<\/span><\/span><\/label><\/div><div class=\"yop-poll-answer-row\"><label class=\"yop-poll-answer\"><input type=\"radio\" name=\"yop-poll-44-44\" value=\"377\" data-yop-sub=\"377\" \/><span class=\"yop-poll-answer-text\"><span>g<\/span><\/span><\/label><\/div><div class=\"yop-poll-answer-row\"><label class=\"yop-poll-answer\"><input type=\"radio\" name=\"yop-poll-44-44\" value=\"378\" data-yop-sub=\"378\" \/><span class=\"yop-poll-answer-text\"><span>h<\/span><\/span><\/label><\/div><div class=\"yop-poll-answer-row\"><label class=\"yop-poll-answer\"><input type=\"radio\" name=\"yop-poll-44-44\" value=\"379\" data-yop-sub=\"379\" \/><span class=\"yop-poll-answer-text\"><span>i<\/span><\/span><\/label><\/div><div class=\"yop-poll-answer-row\"><label class=\"yop-poll-answer\"><input type=\"radio\" name=\"yop-poll-44-44\" value=\"380\" data-yop-sub=\"380\" \/><span class=\"yop-poll-answer-text\"><span>j<\/span><\/span><\/label><\/div><\/div><\/fieldset><\/div><div class=\"yop-poll-footer yop-poll-footer--center\"><div class=\"yop-poll-actions\"><button type=\"button\" class=\"yop-poll-vote-button has-background has-text-color\" data-yop-vote data-yop-perm=\"wordpress\" data-yop-signed-in-label=\"\u2192\">Sign in with WordPress<\/button><\/div><\/div><\/div><noscript><p class=\"yop-poll-noscript\">Voting in this poll requires JavaScript.<\/p><\/noscript><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><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}]}}