Write down the value of the Boltzmann’s constant kb. It has the dimension of energy divided by temperature (T). At which value of T (in degrees Kelvin) is kBT equal to: 1 Joule, 1 Calorie, 1 electron volt, the ionization energy of the helium atom, the energy of one photon with a wave length of 5000 angstrom, the kinetic energy of one helium molecule with a velocity of 500 m\/s? The first law of thermodynamics, AU = -W+Q, is a statement of unification of calorime- try with mechanics; that heat Q is a form of energy. W and Q are typically of the same order of magnitude in processes involving gases (like weather and gasoline engines), but for liquids and solids it is typically true that W < q.=”” this=”” disparity=”” is=”” the=”” reason=”” why=”” the=”” identification=”” of=”” heat=”” with=”” energy=”” was=”” obscured=”” until=”” the=”” 18th=”” century.=”” friction=”” does=”” not=”” heat-up=”” an=”” object=”” significantly=”” unless=”” you=”” start=”” doing=”” things=”” like=”” boring=”” canons=”” (rumfeld).=”” it=”” also=”” means=”” that=”” a=”” gasoline=”” engine=”” and=”” our=”” body=”” can=”” perform=”” lots=”” of=”” work=”” while=”” burning=”” (oridizing)=”” only=”” small=”” amounts=”” of=”” oil=”” or=”” chocolate.=”” here=”” are=”” a=”” few=”” more=””><\/p>\n\n\n\n
a. What is the value of the specific heat of water at room temperature and one atmosphere? What is the value of the latent heat of vaporization at the boiling point of water at one atmosphere? b. Imagine a bucket of water at T = 20\u00b0 C. How fast do you have to throw the water from the bucket onto a wall for it to reach the boiling point on impact assuming the process is adiabatic and the water sticks and does not splash back? c. How much faster do you have to throw it for all the water to boil away into water-vapor on impact?<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n he Boltzmann constant (k\u2086) is a fundamental physical constant that relates the average kinetic energy of particles in a gas to the temperature of the gas.ts value is exactly 1.380649 \u00d7 10\u207b\u00b2\u00b3 joules per kelvin (J\/K).\ue200cite\ue202turn0search2\ue201 = E \/ k\u2086 Write down the value of the Boltzmann’s constant kb. It has the dimension of energy divided by temperature (T). At which value of T (in degrees Kelvin) is kBT equal to: 1 Joule, 1 Calorie, 1 electron volt, the ionization energy of the helium atom, the energy of one photon with a wave length of […]<\/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-187874","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187874","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=187874"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/187874\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=187874"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=187874"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=187874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
To determine the temperature (T) at which k\u2086T equals specific energy values, we can rearrange the equation k\u2086T = E to solve for T:<\/p>\n\n\n\n
Applying this formula:<\/p>\n\n\n\n\n
= 1 J \/ (1.380649 \u00d7 10\u207b\u00b2\u00b3 J\/K) \u2248 7.24297 \u00d7 10\u00b2\u00b2 K<\/li>\n\n\n\n
ince 1 calorie = 4.184 joules, = 4.184 J \/ (1.380649 \u00d7 10\u207b\u00b2\u00b3 J\/K) \u2248 3.031 \u00d7 10\u00b2\u00b2 K<\/li>\n\n\n\n
eV = 1.602176634 \u00d7 10\u207b\u00b9\u2079 joules, = 1.602176634 \u00d7 10\u207b\u00b9\u2079 J \/ (1.380649 \u00d7 10\u207b\u00b2\u00b3 J\/K) \u2248 1.16045 \u00d7 10\u2074 K<\/li>\n\n\n\n
he ionization energy of helium is approximately 79 eV, hich is 79 \u00d7 1.602176634 \u00d7 10\u207b\u00b9\u2079 J \u2248 1.26572 \u00d7 10\u207b\u00b9\u2077 J. = 1.26572 \u00d7 10\u207b\u00b9\u2077 J \/ (1.380649 \u00d7 10\u207b\u00b2\u00b3 J\/K) \u2248 9.16832 \u00d7 10\u2075 K<\/li>\n\n\n\n
he energy (E) of a photon is given by E = hc\/\u03bb, here h is Planck’s constant (6.62607015 \u00d7 10\u207b\u00b3\u2074 J\u00b7s), is the speed of light (2.99792458 \u00d7 10\u2078 m\/s), nd \u03bb is the wavelength in meters. or \u03bb = 5000 \u00c5 = 5000 \u00d7 10\u207b\u00b9\u2070 m = 5 \u00d7 10\u207b\u2077 m, = (6.62607015 \u00d7 10\u207b\u00b3\u2074 J\u00b7s \u00d7 2.99792458 \u00d7 10\u2078 m\/s) \/ 5 \u00d7 10\u207b\u2077 m 3.97289 \u00d7 10\u207b\u00b9\u2079 J. = 3.97289 \u00d7 10\u207b\u00b9\u2079 J \/ (1.380649 \u00d7 10\u207b\u00b2\u00b3 J\/K) \u2248 2.877 \u00d7 10\u00b3 K<\/li>\n\n\n\n
he kinetic energy (KE) is given by KE = \u00bdmv\u00b2, here m is the mass and v is the velocity. he mass of a helium atom is approximately 4.002602 u, here 1 atomic mass unit (u) = 1.66053906660 \u00d7 10\u207b\u00b2\u2077 kg, o m \u2248 4.002602 \u00d7 1.66053906660 \u00d7 10\u207b\u00b2\u2077 kg \u2248 6.64648 \u00d7 10\u207b\u00b2\u2077 kg. E = 0.5 \u00d7 6.64648 \u00d7 10\u207b\u00b2\u2077 kg \u00d7 (500 m\/s)\u00b2 0.5 \u00d7 6.64648 \u00d7 10\u207b\u00b2\u2077 kg \u00d7 2.5 \u00d7 10\u2075 (m\u00b2\/s\u00b2) 8.3081 \u00d7 10\u207b\u00b2\u00b2 J. = 8.3081 \u00d7 10\u207b\u00b2\u00b2 J \/ (1.380649 \u00d7 10\u207b\u00b2\u00b3 J\/K) \u2248 6.017 \u00d7 10\u00b9 K
hese calculations illustrate the temperatures at which the thermal energy (k\u2086T) corresponds to various specific energy values.t’s important to note that these temperatures are theoretical and serve to provide insight into the relationship between temperature and energy at the molecular and atomic levels.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"