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Physical Chemistry

What is Physical Chemistry?

Chemistry is an interdisciplinary science concerned with studying the properties of matter and the way substances interact with each other. Physical chemistry combines chemistry findings with physics. It aims to explain the principles of matter interactions and energy exchange at the atomic and molecular level. A degree in physical chemistry enables people to find employment in many sectors that use physical and chemical principles and experimental methods such as science, technical, or medical institutes or development control labs in the pharmaceutical, chemical, food, or other industries. Physical chemists can also work as teachers and professors at many schools or universities that teach physical chemistry or related subjects. Physical chemistry has several branches, but the most well-known branch is called thermodynamics.

What is Thermodynamics?

Thermodynamics is a science concerned with studying principles behind energy and changes in energy. Thermodynamics was developed to understand heat as one of the two principle processes (apart from work), especially the work of heat engines and the conversion of heat. Thermodynamics not only studies heat as a physical phenomenon, but also the chemical reactions that result in heat production or removal. This science can give answers to questions related to the outcome of the chemical interaction, the concentrations of products and reactants following the reaction, and the amount of heat that will be produced during these reactions. Thermodynamics gives scientists information on the ways energy is stored, transferred, released or used. However, thermodynamics does not provide answers related to the time needed for chemical reactions to take place, nor the mechanisms of such reactions.

What is the First Law of Thermodynamics?

The First Law of Thermodynamics explains the fundamental concepts of energy, work, and heat as well as the relation between these three elements. There are two versions of this law. The simpler version states: “Energy is conserved.” The more complex version explains “Energy can neither be created nor destroyed. However, it can be transformed from one form to another. ” There is one additional definition of the first law of thermodynamics that is based on Einstein’s theory of relativity. In his equation E= mc², Einstein explained that mass and energy correlate with each other. Therefore, the first law of thermodynamics can be formulated as follows: “The total mass and energy of an isolated system remain unchanged ” or “The total energy of a system and its surroundings must remain constant; however, it can change from one form to another. ”

Can the First Law of Thermodynamics be expressed through a Mathematical Equation?

The First Law of Thermodynamics can be explained through the statement of the following mathematical scenario: A system in its initial state and with internal energy E1 receives heat q that can either increase its internal energy, be used for work, or both. In the event that heat q increases the internal energy, the whole system’s energy value changes to E2. The mathematical formula that describes this relationship is as follows: E2 – E1 = delta E (a total increase in internal energy).

If the amount of work done by the system is labelled with W, then the law of conservation of energy would suggest the amount of heat absorbed by the system equals the sum of the increase in internal energy of the system and work done by the system:

delta E + (–W) = delta E – W or delta E = q + W .

The minus sign of work (–W) is used to mark the work done by the system in the surroundings. It suggests that the internal energy of the system decreases with work. It also indicates that when a system receives a certain amount of heat “q”,and performs a certain amount of work “W”, its internal energy increases by delta E. For small infinitesimal changes, the previous equation can be written as follows: delta E = delta q + delta W... where delta q is the amount of heat given to the system, delta E represents infinitesimal changes in the internal energy and delta W represents the work done by the system. If only considering expansion work (pressure-volume work) as the work resulting from a change in volume, then the equation would go as follows: delta W = –P delta V.

References

Kirshenbaum, G. S., Pearce, E. M., & Zaikov, G. E. (2012). New Steps in Physical Chemistry, Chemical Physics, and Biochemical Physics. Hauppauge, N.Y.: Nova Science Publishers, Inc.

Mortimer, R. G. (2005). Mathematics for Physical Chemistry. Burlington, Mass: Academic Press.

Singh, N. B. (2009). Physical Chemistry. New Delhi: New Age International.

Linder, B. (2011). Elementary Physical Chemistry. Singapore: World Scientific.

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eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (161μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (26μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (14μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (10μs)
Illuminate\Database\Events\StatementPrepared (788μs)
Illuminate\Database\Events\QueryExecuted (1.01ms)
eloquent.retrieved: App\Models\Subject (119μs)
Illuminate\Database\Events\StatementPrepared (703μs)
Illuminate\Database\Events\QueryExecuted (1.17ms)
eloquent.retrieved: App\Models\SubjectCat (184μs)
creating: components.homework-blocks (287μs)
composing: components.homework-blocks (115μs)
creating: site.blocks.reviews (976μs)
composing: site.blocks.reviews (22μs)
creating: site.blocks.submit-homework (149μs)
composing: site.blocks.submit-homework (20μs)
creating: site.blocks.faq (113μs)
composing: site.blocks.faq (17μs)
eloquent.booting: App\Models\Twill\TwillFaq (347μs)
eloquent.booted: App\Models\Twill\TwillFaq (202μs)
eloquent.booting: App\Models\Twill\Slugs\TwillFaqSlug (309μs)
eloquent.booted: App\Models\Twill\Slugs\TwillFaqSlug (76μs)
Illuminate\Database\Events\StatementPrepared (11.61ms)
Illuminate\Database\Events\QueryExecuted (1.18ms)
eloquent.retrieved: App\Models\Twill\TwillFaq (186μs)
Illuminate\Database\Events\StatementPrepared (907μs)
Illuminate\Database\Events\QueryExecuted (856μs)
eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (115μs)
eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (23μs)
creating: components.faq-item (161μs)
composing: components.faq-item (123μs)
Illuminate\Database\Events\StatementPrepared (4.42ms)
Illuminate\Database\Events\QueryExecuted (1.09ms)
eloquent.retrieved: App\Models\Twill\TwillFaq (136μs)
Illuminate\Database\Events\StatementPrepared (755μs)
Illuminate\Database\Events\QueryExecuted (1.47ms)
eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (91μs)
eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (22μs)
creating: components.faq-item (234μs)
composing: components.faq-item (55μs)
Illuminate\Database\Events\StatementPrepared (1.39ms)
Illuminate\Database\Events\QueryExecuted (917μs)
eloquent.retrieved: App\Models\Twill\TwillFaq (109μs)
Illuminate\Database\Events\StatementPrepared (5.84ms)
Illuminate\Database\Events\QueryExecuted (4.46ms)
eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (114μs)
creating: components.faq-item (105μs)
composing: components.faq-item (58μs)
Illuminate\Database\Events\StatementPrepared (1.27ms)
Illuminate\Database\Events\QueryExecuted (1.21ms)
eloquent.retrieved: App\Models\Twill\TwillFaq (135μs)
Illuminate\Database\Events\StatementPrepared (703μs)
Illuminate\Database\Events\QueryExecuted (815μs)
eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (80μs)
creating: components.faq-item (89μs)
composing: components.faq-item (53μs)
creating: site.blocks.text-with-image (319μs)
composing: site.blocks.text-with-image (22μs)
creating: site.blocks.work-with-tutors (189μs)
composing: site.blocks.work-with-tutors (20μs)
creating: site.layouts.app (211μs)
composing: site.layouts.app (20μs)
creating: components.canonical (365μs)
composing: components.canonical (100μs)
creating: components.open-graph (193μs)
composing: components.open-graph (81μs)
creating: site.headers.header (253μs)
composing: site.headers.header (81μs)
Illuminate\Cache\Events\CacheHit (1.82ms)
creating: components.footer (85μs)
composing: components.footer (169μs)
Illuminate\Cache\Events\CacheHit (889μs)
Illuminate\Cache\Events\CacheHit (293μs)
Illuminate\Cache\Events\CacheHit (251μs)
Illuminate\Cache\Events\CacheHit (202μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (278μs)
Illuminate\Cache\Events\CacheHit (226μs)
Illuminate\Cache\Events\CacheHit (309μs)
Illuminate\Cache\Events\CacheHit (12.58ms)
Illuminate\Cache\Events\CacheHit (475μs)
Illuminate\Cache\Events\CacheHit (221μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (316μs)
creating: components.forms.contact-us (285μs)
composing: components.forms.contact-us (458μs)
creating: components.forms.get-started (178μs)
composing: components.forms.get-started (234μs)
creating: components.forms.free-tool-download (132μs)
composing: components.forms.free-tool-download (185μs)
creating: components.forms.claim-free-worksheet (132μs)
composing: components.forms.claim-free-worksheet (77μs)
creating: components.forms.tutor-subscription-waitlist (96μs)
composing: components.forms.tutor-subscription-waitlist (65μs)
creating: components.forms.tutor-subscription-join (101μs)
composing: components.forms.tutor-subscription-join (62μs)
creating: components.forms.tutor-support (257μs)
composing: components.forms.tutor-support (279μs)

271 x Illuminate\Cache\Events\CacheHit (18.23%)	217ms
28 x Illuminate\Database\Events\StatementPrepared (11.26%)	134ms
28 x Illuminate\Database\Events\QueryExecuted (8.54%)	102ms
5 x Illuminate\Cache\Events\CacheMissed (2.89%)	34.39ms
5 x Illuminate\Cache\Events\KeyWritten (2.31%)	27.52ms
6 x creating: components.tutors-card (1.3%)	15.49ms
1 x Illuminate\Foundation\Events\LocaleUpdated (0.26%)	3.04ms
2 x Illuminate\Database\Events\ConnectionEstablished (0.17%)	2.06ms
1 x Illuminate\Routing\Events\Routing (0.12%)	1.43ms
6 x eloquent.retrieved: App\Models\User\Tutor (0.12%)	1.38ms
1 x creating: site.blocks.reviews (0.08%)	976μs
8 x eloquent.retrieved: App\Models\SubjectCat (0.08%)	945μs
1 x creating: site.blocks.subject-homework (0.06%)	769μs
1 x eloquent.booting: App\Models\User\TutorAttributes\TutorDegree (0.06%)	726μs
12 x eloquent.retrieved: App\Models\Subject (0.06%)	710μs
1 x eloquent.booting: App\Models\Meta (0.05%)	645μs
6 x composing: components.tutors-card (0.05%)	593μs
4 x creating: components.faq-item (0.05%)	589μs
1 x eloquent.booting: App\Models\Subject (0.05%)	578μs
4 x eloquent.retrieved: App\Models\Twill\TwillFaq (0.05%)	566μs
1 x eloquent.booting: App\Models\User\Tutor (0.04%)	503μs
1 x creating: components.tutors-cards (0.04%)	486μs
1 x composing: components.forms.contact-us (0.04%)	458μs
6 x eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (0.04%)	445μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)	420μs
1 x Illuminate\Routing\Events\RouteMatched (0.03%)	386μs
1 x creating: components.canonical (0.03%)	365μs
1 x eloquent.booting: App\Models\Twill\TwillFaq (0.03%)	347μs
1 x creating: site.blocks.text-with-image (0.03%)	319μs
1 x eloquent.booting: App\Models\Twill\Slugs\TwillFaqSlug (0.03%)	309μs
4 x composing: components.faq-item (0.02%)	289μs
1 x creating: components.homework-blocks (0.02%)	287μs
1 x creating: components.forms.contact-us (0.02%)	285μs
1 x composing: components.forms.tutor-support (0.02%)	279μs
1 x creating: components.forms.tutor-support (0.02%)	257μs
1 x creating: site.headers.header (0.02%)	253μs
1 x creating: site.blocks.how-it-works (0.02%)	243μs
6 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)	235μs
1 x composing: components.forms.get-started (0.02%)	234μs
1 x creating: components.breadcrumbs (0.02%)	215μs
1 x creating: site.layouts.app (0.02%)	211μs
1 x eloquent.booted: App\Models\Twill\TwillFaq (0.02%)	202μs
1 x creating: components.open-graph (0.02%)	193μs
1 x creating: site.blocks.work-with-tutors (0.02%)	189μs
1 x composing: components.forms.free-tool-download (0.02%)	185μs
1 x creating: components.forms.get-started (0.01%)	178μs
1 x composing: components.footer (0.01%)	169μs
1 x eloquent.booted: App\Models\User\Tutor (0.01%)	165μs
1 x creating: site.blocks.submit-homework (0.01%)	149μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.01%)	145μs
1 x eloquent.booting: App\Models\SubjectCat (0.01%)	138μs
1 x creating: components.forms.free-tool-download (0.01%)	132μs
1 x creating: components.forms.claim-free-worksheet (0.01%)	132μs
1 x composing: components.tutors-cards (0.01%)	121μs
1 x composing: components.homework-blocks (0.01%)	115μs
1 x creating: site.blocks.faq (0.01%)	113μs
1 x creating: site.blocks.subject-tutors (0.01%)	102μs
1 x creating: components.forms.tutor-subscription-join (0.01%)	101μs
1 x composing: components.canonical (0.01%)	100μs
1 x creating: components.forms.tutor-subscription-waitlist (0.01%)	96μs
1 x creating: subjects.show (0.01%)	94μs
1 x composing: site.blocks.how-it-works (0.01%)	93μs
1 x composing: components.breadcrumbs (0.01%)	92μs
1 x creating: components.footer (0.01%)	85μs
1 x composing: subjects.show (0.01%)	83μs
1 x composing: components.open-graph (0.01%)	81μs
1 x composing: site.headers.header (0.01%)	81μs
1 x composing: components.forms.claim-free-worksheet (0.01%)	77μs
1 x eloquent.booted: App\Models\Twill\Slugs\TwillFaqSlug (0.01%)	76μs
1 x eloquent.booted: App\Models\Subject (0.01%)	75μs
1 x eloquent.retrieved: App\Models\Meta (0.01%)	68μs
1 x eloquent.booted: App\Models\User\TutorAttributes\TutorDegree (0.01%)	68μs
1 x composing: components.forms.tutor-subscription-waitlist (0.01%)	65μs
1 x composing: components.forms.tutor-subscription-join (0.01%)	62μs
1 x eloquent.booted: App\Models\Meta (0%)	49μs
1 x eloquent.booted: App\Models\SubjectCat (0%)	44μs
1 x composing: site.blocks.subject-homework (0%)	26μs
1 x composing: site.blocks.reviews (0%)	22μs
1 x composing: site.blocks.text-with-image (0%)	22μs
1 x composing: site.blocks.submit-homework (0%)	20μs
1 x composing: site.blocks.work-with-tutors (0%)	20μs
1 x composing: site.layouts.app (0%)	20μs
1 x composing: site.blocks.faq (0%)	17μs
1 x composing: site.blocks.subject-tutors (0%)	12μs

34 templates were rendered

1x subjects.showshow.blade.phpblade
1x components.breadcrumbsbreadcrumbs.blade.phpblade
1x site.blocks.how-it-workshow-it-works.blade.phpblade
1x site.blocks.subject-tutorssubject-tutors.blade.phpblade
1x components.tutors-cardstutors-cards.blade.phpblade
6x components.tutors-cardtutors-card.blade.phpblade
1x site.blocks.subject-homeworksubject-homework.blade.phpblade
1x components.homework-blockshomework-blocks.blade.phpblade
1x site.blocks.reviewsreviews.blade.phpblade
1x site.blocks.submit-homeworksubmit-homework.blade.phpblade
1x site.blocks.faqfaq.blade.phpblade
4x components.faq-itemfaq-item.blade.phpblade
1x site.blocks.text-with-imagetext-with-image.blade.phpblade
1x site.blocks.work-with-tutorswork-with-tutors.blade.phpblade
1x site.layouts.appapp.blade.phpblade
1x components.canonicalcanonical.blade.phpblade
1x components.open-graphopen-graph.blade.phpblade
1x site.headers.headerheader.blade.phpblade
1x components.footerfooter.blade.phpblade
1x components.forms.contact-uscontact-us.blade.phpblade
1x components.forms.get-startedget-started.blade.phpblade
1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
1x components.forms.tutor-supporttutor-support.blade.phpblade

uri: GET subjects/{categoryUri}/{subjectUri?}
middleware: web, utm.parameters
controller: App\Http\Controllers\SubjectController@show
namespace
where
as: subjects.show
file: app/Http/Controllers/SubjectController.php:43-96

28 statements were executed, 2 of which were duplicates, 26 unique. Show only duplicated166ms

Connection Establishedtwenty4_siteSubjectRepository.php#123

Backtrace

13. app/Repositories/SubjectRepository.php:123
14. app/Http/Controllers/SubjectController.php:54
15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260

select * from `subjects` where `urlFriendlyTitle` = 'Physical-Chemistry' limit 1

13.58mstwenty4_siteSubjectRepository.php#123

Bindings	0: Physical-Chemistry
Backtrace	15. app/Repositories/SubjectRepository.php:123 16. app/Http/Controllers/SubjectController.php:54 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260

select * from `subject_cats` where `subject_cats`.`id` in (36)

1.21mstwenty4_siteSubjectRepository.php#123

Backtrace

20. app/Repositories/SubjectRepository.php:123
21. app/Http/Controllers/SubjectController.php:54
22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260

select * from `meta` where `meta`.`id` = 3 limit 1

1.05mstwenty4_siteMetaService.php#118

Bindings	0: 3
Backtrace	19. app/Services/MetaService.php:118 20. app/Services/MetaService.php:108 21. app/Services/MetaService.php:81 22. app/Http/Controllers/SubjectController.php:89 23. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54

Connection Establishedtwenty4_siteTutorRepository.php#40

Backtrace

13. app/Repositories/TutorRepository.php:40
14. app/View/Components/TutorsCards.php:28
15. app/View/Components/TutorsCards.php:22
17. vendor/laravel/framework/src/Illuminate/Container/Container.php:929
18. vendor/laravel/framework/src/Illuminate/Container/Container.php:770

select count(*) as aggregate from `users` where (`subjectsQualified` like '%|165|%' or `DSF_subjectsQualified` like '%|165|%' or `allsubjects` = 1) and `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor'

22.38mstwenty4_siteTutorsCards.php#35

Bindings	0: %\|165\|% 1: %\|165\|% 2: 1 3: 0 4: 5: 1 6: 0 7: 0 8: 9: tutor
Backtrace	15. app/View/Components/TutorsCards.php:35 16. app/View/Components/TutorsCards.php:22 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:929 19. vendor/laravel/framework/src/Illuminate/Container/Container.php:770 20. vendor/laravel/framework/src/Illuminate/Foundation/Application.php:933

select * from `users` where (`subjectsQualified` like '%|165|%' or `DSF_subjectsQualified` like '%|165|%' or `allsubjects` = 1) and `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor' order by `completed_requests` desc limit 6 offset 0

13.51mstwenty4_siteTutorsCards.php#35

Bindings	0: %\|165\|% 1: %\|165\|% 2: 1 3: 0 4: 5: 1 6: 0 7: 0 8: 9: tutor
Backtrace	15. app/View/Components/TutorsCards.php:35 16. app/View/Components/TutorsCards.php:22 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:929 19. vendor/laravel/framework/src/Illuminate/Container/Container.php:770 20. vendor/laravel/framework/src/Illuminate/Foundation/Application.php:933

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 26463 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

4.38mstwenty4_siteTutor.php#361

Bindings	0: 26463
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select * from `subject_cats` where `subject_cats`.`id` = 35 limit 1

2.52mstwenty4_siteSubject.php#100

Bindings	0: 35
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 32 limit 1

9.35mstwenty4_siteSubject.php#100

Bindings	0: 32
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 72437 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

8.1mstwenty4_siteTutor.php#361

Bindings	0: 72437
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select * from `subject_cats` where `subject_cats`.`id` = 2 limit 1

12.9mstwenty4_siteSubject.php#100

Bindings	0: 2
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 813 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

7.43mstwenty4_siteTutor.php#361

Bindings	0: 813
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 70526 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

13.78mstwenty4_siteTutor.php#361

Bindings	0: 70526
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 117127 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

2.33mstwenty4_siteTutor.php#361

Bindings	0: 117127
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 69755 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1

1.17mstwenty4_siteTutor.php#361

Bindings	0: 69755
Backtrace	18. app/Models/User/Tutor.php:361 19. view::components.tutors-card:11 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69

select `subjects`.*, `subject_cats`.`title` as `category_title`, `subject_cats`.`id` as `category_id` from `subjects` inner join `subject_cats` on `subject_cats`.`id` = `subjects`.`catID` where `subjects`.`id` in (87, 13, 359, 90, 165, 6, 401, 14, 226, 269)

2.9mstwenty4_siteTutor.php#214

Bindings	0: 87 1: 13 2: 359 3: 90 4: 165 5: 6 6: 401 7: 14 8: 226 9: 269
Backtrace	14. app/Models/User/Tutor.php:214 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 18. app/Models/User/Tutor.php:216 24. app/Models/User/Tutor.php:267

select * from `subject_cats` where `subject_cats`.`id` in (1, 34, 36)

1.29mstwenty4_siteTutor.php#214

Backtrace

19. app/Models/User/Tutor.php:214
20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
23. app/Models/User/Tutor.php:216
29. app/Models/User/Tutor.php:267

select count(*) as aggregate from `solutionslibrary` where exists (select * from `subjects` where `solutionslibrary`.`subject` = `subjects`.`id`) and `subject` = 165 and `status` = 'published' and `price` > 0

11.2mstwenty4_siteHomeworkBlocks.php#27

Bindings	0: 165 1: published 2: 0
Backtrace	15. app/View/Components/HomeworkBlocks.php:27 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.subject-homework:4 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `solutionslibrary` where exists (select * from `subjects` where `solutionslibrary`.`subject` = `subjects`.`id`) and `subject` = 165 and `status` = 'published' and `price` > 0 order by `purchase_count` desc limit 6 offset 0

3.61mstwenty4_siteHomeworkBlocks.php#27

Bindings	0: 165 1: published 2: 0
Backtrace	15. app/View/Components/HomeworkBlocks.php:27 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.subject-homework:4 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `subjects` where `subjects`.`id` in (165)

1.1mstwenty4_siteHomeworkBlocks.php#27

Backtrace

20. app/View/Components/HomeworkBlocks.php:27
21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
22. view::site.blocks.subject-homework:4
24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `subject_cats` where `subject_cats`.`id` in (36)

1.11mstwenty4_siteHomeworkBlocks.php#27

Backtrace

25. app/View/Components/HomeworkBlocks.php:27
26. vendor/laravel/framework/src/Illuminate/View/Component.php:102
27. view::site.blocks.subject-homework:4
29. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
30. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'can-you-help-me-with-my-homework-in-less-than-24-hours' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1

11.77mstwenty4_siteFaqItem.php#15

Bindings	0: can-you-help-me-with-my-homework-in-less-than-24-hours 1: 1 2: en
Backtrace	15. app/View/Components/FaqItem.php:15 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.faq:7 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (1) and `twill_faq_slugs`.`deleted_at` is null

900μstwenty4_siteFaqItem.php#15

Backtrace

20. app/View/Components/FaqItem.php:15
21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
22. view::site.blocks.faq:7
24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'can-you-help-me-with-my-examquiztest' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1

4.05mstwenty4_siteFaqItem.php#15

Bindings	0: can-you-help-me-with-my-examquiztest 1: 1 2: en
Backtrace	15. app/View/Components/FaqItem.php:15 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.faq:24 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (2) and `twill_faq_slugs`.`deleted_at` is null

1.51mstwenty4_siteFaqItem.php#15

Backtrace

20. app/View/Components/FaqItem.php:15
21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
22. view::site.blocks.faq:24
24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'how-much-will-it-cost' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1

1mstwenty4_siteFaqItem.php#15

Bindings	0: how-much-will-it-cost 1: 1 2: en
Backtrace	15. app/View/Components/FaqItem.php:15 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.faq:41 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (3) and `twill_faq_slugs`.`deleted_at` is null

9.55mstwenty4_siteFaqItem.php#15

Backtrace

20. app/View/Components/FaqItem.php:15
21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
22. view::site.blocks.faq:41
24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'what-kind-of-payments-do-you-accept' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1

1.01mstwenty4_siteFaqItem.php#15

Bindings	0: what-kind-of-payments-do-you-accept 1: 1 2: en
Backtrace	15. app/View/Components/FaqItem.php:15 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102 17. view::site.blocks.faq:58 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (4) and `twill_faq_slugs`.`deleted_at` is null

880μstwenty4_siteFaqItem.php#15

Backtrace

20. app/View/Components/FaqItem.php:15
21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
22. view::site.blocks.faq:58
24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58

App\Models\Subject: 12Subject.php
App\Models\SubjectCat: 8SubjectCat.php
App\Models\User\Tutor: 6Tutor.php
App\Models\HomeworkLibrary\HomeworkLibrary: 6HomeworkLibrary.php
App\Models\Twill\Slugs\TwillFaqSlug: 6TwillFaqSlug.php
App\Models\Twill\TwillFaq: 4TwillFaq.php
App\Models\Meta: 1Meta.php

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