{"id":2233,"date":"2023-10-02T11:21:08","date_gmt":"2023-10-02T11:21:08","guid":{"rendered":"http:\/\/localhost\/ecole9ja\/?p=2233"},"modified":"2023-10-02T11:23:36","modified_gmt":"2023-10-02T11:23:36","slug":"week-4-ss1-second-term-physics-notes","status":"publish","type":"post","link":"https:\/\/ecolebooks.com\/nigeria\/posts\/week-4-ss1-second-term-physics-notes\/","title":{"rendered":"Week 4 &#8211; SS1 Second Term Physics Notes"},"content":{"rendered":"<p>\u00a0<strong>WEEK FOUR<br \/>\n<\/strong><strong>TOPIC: Expansivity and Its Application \u2013 Linear, Area and Volume. Anomalous<br \/>\n<\/strong><strong>Expansion of Water. Real and Apparent Expansivity<\/strong><br \/>\n\t\t<strong>CONTENT<br \/>\n<\/strong><\/p>\n<ul>\n<li>\n<div><strong>Linear Expansivity of Solid<br \/>\n<\/strong><\/div>\n<\/li>\n<li>\n<div><strong>Area Expansivity of Solid<br \/>\n<\/strong><\/div>\n<\/li>\n<li>\n<div><strong>Cubic Expansivity of solid and Liquid<br \/>\n<\/strong><\/div>\n<\/li>\n<li>\n<div><strong>Anomalous Behavior of Water<br \/>\n<\/strong><\/div>\n<p><strong>Linear Expansivity<br \/>\n<\/strong><\/li>\n<\/ul>\n<p>Linear expansivity of a solid can be defined as increase in length per unit length, per unit degree rise in temperature. It is denoted by (\u03b1) and measure in per Kelvin or per degree Celsius.<br \/>\nMathematical representation<br \/>\n\u00a0\u00a0\u00a0\u00a0\u03b1=     L<sub>2<\/sub> \u2013 L<sub>1<\/sub>\u00a0\u00a0\u00a0\u00a0<br \/>\n\u00a0\u00a0\u00a0\u00a0         L<sub>1<\/sub> (\u04e8<sub>2<\/sub> &#8211; \u04e8<sub>1<\/sub>)  ______________ (i)<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1121_Week4SS1Se1.png\" alt=\"\"\/>Linear expansivity (\u03b1)= increase in length\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<br \/>\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0    Unit length x temp change<br \/>\nL<sub>1<\/sub> is the original length \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u04e8<sub>1<\/sub> is the initial temperature<br \/>\nL<sub>2<\/sub> is the final length\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u04e8<sub>2<\/sub> is the final temperature<br \/>\n\u25b2L = L<sub>2<\/sub> \u2013 L<sub>1<\/sub><br \/>\n\t\t\u25b2\u04e8 = \u04e8<sub>2<\/sub> &#8211; \u04e8<sub>1<\/sub>                                                 \u03b1 = \u25b2L<br \/>\n\t\t                                                                                L<sub>1<\/sub><br \/>\n\t\t\u25b2\u04e8        ________ (ii)<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1121_Week4SS1Se2.png\" alt=\"\"\/>\u03b1 = L<sub>2<\/sub> \u2013 L<sub>1<\/sub><br \/>\n\t\t      L<sub>1<\/sub> X \u25b2\u04e8<br \/>\nL<sub>2<\/sub> \u2013 L1 = \u03b1 L<sub>1<\/sub><br \/>\n\t\t\u25b2\u04e8<br \/>\nL<sub>2<\/sub> = L<sub>1<\/sub> + X L<sub>1<\/sub><br \/>\n\t\t\u25b2\u04e8<br \/>\nL<sub>2<\/sub> = L<sub>1<\/sub> (1 + X \u25b2\u04e8)<br \/>\nN.B. \u25b2L = L<sub>2<\/sub> \u2013 L<sub>1<\/sub><\/p>\n<p>\t\t\u25b2\u04e8 = \u04e8<sub>2<\/sub> &#8211; \u04e8<sub>1<\/sub><\/p>\n<ol>\n<li>\n<div>A brass rod is 2m long at a certain temperature. What will be the length for a temperature rise of 100K , if the linear expansivity of brass 18 x 10-6K<sup>-1<\/sup>\n\t\t\t\t<\/div>\n<p>SOLUTION<br \/>\nL1 = 2m,      L<sub>2<\/sub> =?,     \u25b2\u04e8 = 100K,     \u03b1 = 18x1o-6k-1<br \/>\nL<sub>2<\/sub> = L1 (1 + \u03b1\u25b2\u04e8)<br \/>\nL<sub>2<\/sub> = 2 (1 + (18 X 10-6 X 100)<br \/>\n= 2(1 + 0.00018<br \/>\n= 2 (1.OOO18)<br \/>\n= 2.0036m<\/p>\n<p>\u00a0<\/li>\n<\/ol>\n<p><strong>Area Expansivity<br \/>\n<\/strong>The area\/superficial expansivity is the increase in area of per unit area per degree rise in temperature. It is donated by (\u03b2) and measured in per Kelvin and per 8C<br \/>\n<img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1121_Week4SS1Se3.png\" alt=\"\"\/>\u03b2 = \u00a0\u00a0\u00a0\u00a0A<sub>2<\/sub> \u2013 A<sub>1<\/sub><br \/>\n\t\t      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0A<sub>1<\/sub> (\u04e8<sub>2<\/sub> &#8211; \u04e8<sub>1<\/sub>)<br \/>\nRecall; L<sub>2<\/sub> = L<sub>1<\/sub> (1 + \u03b1 \u25b2 \u04e8)<br \/>\nSimilarly b<sub>2<\/sub> = b<sub>1<\/sub> (1 + \u03b1 \u25b2 \u04e8)<br \/>\nA<sub>2<\/sub> = L<sub>1<\/sub> (1 + \u03b1 \u25b2 \u04e8) X b<sub>1<\/sub> (1 + \u03b1 \u25b2 \u04e8)<br \/>\n     = L<sub>1<\/sub>b<sub>1<\/sub> (1 + \u03b1 \u25b2 \u04e8) (1 + \u03b1 \u25b2 \u04e8)<br \/>\nA<sub>2 <\/sub>= A<sub>1<\/sub> (1 + 2 \u03b1 \u25b2 \u04e8 + (\u03b1 \u25b2\u04e8) \u00b2<br \/>\nA<sub>2<\/sub> = A<sub>1<\/sub> (1 + 2 \u03b1 \u25b2 \u04e8)<br \/>\nA<sub>2<\/sub> = A<sub>1<\/sub> (1 + \u03b2 \u25b2 \u04e8)<\/p>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>A brass rod is 2m long at a certain temperature. What will be its length for a temperature rise of 90K, if the linear expansivity of brass is 1.8 x 10-6K<sup>-1<br \/>\n<\/sup><\/div>\n<\/li>\n<li>\n<div>Prove that A<sub>2<\/sub> = A<sub>1<\/sub>(1 + \u03b2\u25b2 \u04e8).\n<\/div>\n<p>\u00a0<br \/>\n\u00a0<strong>Volume\/Cubic Expansivity<br \/>\n<\/strong><\/li>\n<\/ol>\n<p>It is denoted by (Y). It is the increase in volume per unit volume per degree rise in<br \/>\ntemperature<strong><br \/>\n\t\t\t<\/strong><img decoding=\"async\" align=\"left\" src=\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1121_Week4SS1Se4.png\" alt=\"\"\/>Y = V<sub>2<\/sub> \u2013 V<sub>1<\/sub><br \/>\n\t\t       V1 (\u04e8<sub>2<\/sub> &#8211; \u04e8<sub>1<\/sub>)           ___________ (i)<br \/>\nY = 3\u03b1 _________ (ii)<br \/>\nRelationship between \u03b1: \u03b2: Y: = 1: 2<\/p>\n<p>\u00a0<strong>Real and Apparent Cubic Expansivity of Water<\/strong><br \/>\n\t\tReal or absolute cubic expansivity (Yr) .The real \/ absolute of the liquid is the increase in volume by unit volume per degree rise in temperature.<br \/>\nApparent Cubic Expansivity (Ya)<br \/>\nThe apparent cubic expansivity is the increase in volume per unit rise when heated in an expansible vessel.<br \/>\nYr = Ya + Y<\/p>\n<p>\u00a0<strong>Anomalous Behaviour of Water<\/strong><br \/>\n\t\tMost liquid except water expand when heated. This abnormal behavior of water is what is refer to as anomalous expansion of water. When water is heated from 0<sup>0<\/sup>C, it contracts until it reaches 4<sup>0<\/sup>C and beyond this point, water expands normally. The anomalous expansion of water takes place between 0<sup>0<\/sup>C and 4<sup>0<\/sup>C.<\/p>\n<p>\u00a0<strong>EVALUATION<br \/>\n<\/strong><\/p>\n<ol>\n<li>\n<div>With the aid of a diagram, explain the anomalous behavior of water.\n<\/div>\n<\/li>\n<li>\n<div>Describe an experiment to determine the apparent cubic expansivity of a liquid\n<\/div>\n<p>\u00a0<strong>Reading Assignment<br \/>\n<\/strong>New School Physics pg 38 \u2013 40,43 \u2013 46<\/p>\n<p>\u00a0<strong>WEEKEND ASSIGNMENT<br \/>\n<\/strong><\/li>\n<li>\n<div>The anomalous expansion of water takes place between\/at \u2026\u2026\u2026\u2026\u2026\u2026..A. 1<sup>0<\/sup>C and 4<sup>0<\/sup>C B. 0<sup>0<\/sup>C and 4<sup>0<\/sup>C C. 4<sup>0<\/sup>C and 25<sup>0<\/sup>C D. all temperature\n<\/div>\n<\/li>\n<li>\n<div>The SI unit of linear expansivity is \u2026\u2026\u2026 A. per Celsius B. per Fahrenheit C. per Kelvin D. per Joules\n<\/div>\n<\/li>\n<li>\n<div>If the linear expansivity of a solid is 1.8 X 10 <sup>-6<\/sup> k<sup>-1<\/sup>, the area expansivity will be\n<\/div>\n<p>A.0.9 X 10 <sup>-6<\/sup> B. 3.6 X 10 <sup>-6<\/sup> C. 1.8 X 10 <sup>-6<\/sup> D. 5.4 X 10<sup>-6<br \/>\n<\/sup><\/li>\n<li>\n<div>A metal of length 15.01m is heated until its temperature rises by 60<sup>0<\/sup>C. If its new length is 15.05, calculate its linear expansivity\n<\/div>\n<p>A. 0.0004\/K B. 0.00004\/K C. 0.004\/K D. 0.04\/K\n<\/li>\n<li>\n<div>The increase in volume of 10cm<sup>3<\/sup> of mercury when the temperature rises by 100<sup>0<\/sup>C is 0.182cm<sup>3<\/sup>. What is the cubic expansivity of mercury A. 0.000182\/K\n<\/div>\n<p>B. 0.0000182\/K C. 0.000187\/K D. 0.000178\/K<\/p>\n<p>\u00a0<strong>THEORY<\/strong>\n\t\t\t\t<\/li>\n<li>\n<div>Explain the anomalous behavior of water\n<\/div>\n<\/li>\n<li>\n<div>If a cube metal box made of iron of side 2cm is to be used for construction, and the expected temperature difference is 90<sup>0<\/sup>C. What will be the expected change in volume of the cube box if the linear expansivity of iron is 1.25 X 10<sup>-5<\/sup>.\n<\/div>\n<p>\u00a0<br \/>\n\t\t\t\t\u00a0<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u00a0WEEK FOUR TOPIC: Expansivity and Its Application \u2013 Linear, Area and Volume. Anomalous Expansion of&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,191],"tags":[],"class_list":["post-2233","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-ss1-physics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2233","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=2233"}],"version-history":[{"count":1,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2233\/revisions"}],"predecessor-version":[{"id":2234,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2233\/revisions\/2234"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2233"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2233"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}