{"id":197083,"date":"2025-03-06T15:03:05","date_gmt":"2025-03-06T15:03:05","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=197083"},"modified":"2025-03-06T15:03:08","modified_gmt":"2025-03-06T15:03:08","slug":"a-hair-dryer-is-basically-a-duct-in-which-a-few-layers-of-electric-resistors-are-placed","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/06\/a-hair-dryer-is-basically-a-duct-in-which-a-few-layers-of-electric-resistors-are-placed\/","title":{"rendered":"A hair dryer is basically a duct in which a few layers of electric resistors are placed"},"content":{"rendered":"\n<p>A hair dryer is basically a duct in which a few layers of electric resistors are placed. A small fan pulls the air in and forces it to flow over the resistors where it is heated. Air enters a 900-W hair dryer at 100 kPa and 25\u00b0C, and leaves at 50\u00b0C. The cross-sectional area of the hair dryer at the exit is 60 cm2. Neglecting the power consumed by the fan and the heat losses through the walls of the hair dryer, determine<\/p>\n\n\n\n<p>(a) the volume flow rate of air at the inlet and<\/p>\n\n\n\n<p>(b) the velocity of the air at the exit.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-378.png\" alt=\"\" class=\"wp-image-197084\"\/><\/figure>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To analyze the performance of a 900-W hair dryer, we can determine:<\/p>\n\n\n\n<p>(a) the volume flow rate of air at the inlet, and\ue206<\/p>\n\n\n\n<p>(b) the velocity of air at the exit.\ue206<\/p>\n\n\n\n<p><strong>Assumptions:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Air behaves as an ideal gas.\ue206<\/li>\n\n\n\n<li>Negligible heat losses through the hair dryer walls.\ue206<\/li>\n\n\n\n<li>Negligible power consumption by the fan.\ue206<\/li>\n<\/ul>\n\n\n\n<p><strong>Given Data:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Power input (\ud835\udc4a\u0307): 900 \ue204\ue206<\/li>\n<\/ul>\n\n\n\n<p>-\ue203Inlet pressure (\ud835\udc43\u2081): 100 ka\ue204\ue206<\/p>\n\n\n\n<p>\ue203Inlet temperature (\ud835\udc47\u2081): 25\u00b0C = 298.1 K\ue204\ue206<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ue203Exit temperature (\ud835\udc47\u2082): 50\u00b0C = 323.5 K\ue204\ue206<\/li>\n\n\n\n<li>\ue203Exit cross-sectional area (\ud835\udc34\u2082): 60 cm\u00b2 = 0.06 m\u00b2\ue204<\/li>\n\n\n\n<li>\ue203Specific heat capacity of air at constant pressure (\ud835\udc50\u209a): approximately 1.005 k\/kg\u00b7K\ue206<\/li>\n\n\n\n<li>\ue203Gas constant for air (\ud835\udc45): approximately 0.287 J\/kg\u00b7K\ue204\ue206<\/li>\n<\/ul>\n\n\n\n<p><strong>(a) Volume Flow Rate at the Inlet:<\/strong><\/p>\n\n\n\n<p>First, we calculate the mass flow rate (\ud835\udc5a\u0307) using the energy balance eqution:<\/p>\n\n\n\n<p>\ue203\ud835\udc4a\u0307 = \ud835\udc5a\u0307 \u00d7 \ud835\udc50\u209a (\ud835\udc47\u2082 \u2212 \ud835\udc47\u2081)\ue204\ue206<\/p>\n\n\n\n<p>Rarranging:<\/p>\n\n\n\n<p>\ue203\ud835\udc5a\u0307 = \ud835\udc4a\u0307 \/ [\ufffd\u209a \u00d7 (\ud835\udc47\u2082 \u2212 \ud835\udc47\u2081)]\ue204\ue206<\/p>\n\n\n\n<p>Substituting te given values:<\/p>\n\n\n\n<p>\ue203\ud835\udc5a\u0307 = 900 W \/ [1.005 kJ\/kg\u00b7K \u00d7 (32.15K \u2212 298.15 K)]\ue204\ue206<br>\ue203\ud835\udc5a\u0307 \u2248 0.0357 kg\/s\ue204\ue206<\/p>\n\n\n\n<p>Next, we determine the specific volume (\ud835\udc63\u2081) at the inlet usingthe ideal gas law:<br>\ue203\ud835\udc63\u2081 = (\ud835\udc45 \u00d7 \ud835\udc47\u2081) \/ \ud835\udc43\u2081\ue204\ue206<\/p>\n\n\n\n<p>Convrting pressure to kPa:<br>\ue203\ufffd\u2081 = 100 kPa = 100 kPa\ue204\ue206<\/p>\n\n\n\n<p>\ue203\ud835\udc63\u2081 = (0.287 kJkg\u00b7 \u00d7 298.15 K) \/ 10 kPa\ue204\ue206<\/p>\n\n\n\n<p>\ue203\ud835\udc63\u2081 \u2248 0.855 m\u00b3\/kg\ue204\ue206<\/p>\n\n\n\n<p>The volume flow rte (\ud835\udc49\u0307\u2081) at he nlet is:<\/p>\n\n\n\n<p>\ue203\ud835\udc49\u0307\u2081 = \ud835\udc5a\u0307 \u00d7 \ud835\udc63\u2081\ue204\ue206<\/p>\n\n\n\n<p>\ud835\udc49\u0307 = 0.0357 kg\/s \u00d7 .855 m\u00b3\/kg\ue204\ue206<\/p>\n\n\n\n<p>\ue203\ud835\udc49\u0307\u2081 \u2248 0.0305 m\u00b3\/s\ue204\ue206<\/p>\n\n\n\n<p><strong>(b) Velocity of Air at the Exit:<\/strong><\/p>\n\n\n\n<p>First, we calculate the secific volume (\ud835\udc63\u2082 atthe exit:<\/p>\n\n\n\n<p>\ue203\ud835\udc63\u2082 = (\ud835\udc45 \u00d7 \ud835\udc47\u2082) \/ \ud835\udc43\u2081\ue204\ue206<\/p>\n\n\n\n<p>\ue203\ud835\udc63 = 0.287 kJ\/kg\u00b7K \u00d7 23.15 K) \/ 100 kPa\ue204\ue206<\/p>\n\n\n\n<p>\ue203\ud835\udc63\u2082 \u2248 0.928 m\u00b3\/kg\ue204\ue206<\/p>\n\n\n\n<p>Thevolume flow rte \ud835\udc49\u0307\u2082) at the exit is:<\/p>\n\n\n\n<p>\ue203\ud835\udc49\u0307\u2082 = \ufffd\u0307 \ud835\udc63\u2082\ue204\ue206<\/p>\n\n\n\n<p>\ue203\ud835\udc49\u0307\u2082 = 00357 kg\/s \u00d7 0.928 m\u00b3\/kg\ue204\ue206<\/p>\n\n\n\n<p>\ue203\ud835\udc49\u0307\u2082 \u2248 0.033 m\u00b3\/s\ue204\ue206<\/p>\n\n\n\n<p>Finaly,the exit velocity (\ud835\udc49\u2082) is:<br>\ue203\ufffd\u2082 = \ud835\udc49\u0307\u2082 \/ \ud835\udc34\ue204\ue206<\/p>\n\n\n\n<p>\ue203\ud835\udc49\u2082 = 0.0331 m\u00b3\/ \/ 0.006 m\u00b2\ue204\ue206<\/p>\n\n\n\n<p>\ue203\ud835\udc49\u2082 \u2248 5.52 m\/s\ue204\ue206<\/p>\n\n\n\n<p><strong>Summary:<\/strong><\/p>\n\n\n\n<p>(a) \ue203The volume flow rte of ar at the inlet is approximately 0.0305 m\u00b3\/s.\ue204\ue206<\/p>\n\n\n\n<p>(b) \ue203The vlocty of air at the exit is approximately 5.52 m\/s.\ue204\ue206<\/p>\n\n\n\n<p>\ue203These calculations provide insight into the thermodynamic behavior of the hair dryer, illustrating how electrical energy input translates into themal energy, affecting air flow rates and velocities.\ue204\ue206<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A hair dryer is basically a duct in which a few layers of electric resistors are placed. A small fan pulls the air in and forces it to flow over the resistors where it is heated. Air enters a 900-W hair dryer at 100 kPa and 25\u00b0C, and leaves at 50\u00b0C. The cross-sectional area of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-197083","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/197083","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=197083"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/197083\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=197083"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=197083"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=197083"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}