Question
8. General Problem Information:
A commercial plastic manufacturing process in Boston, MA requires a flow of 0.2 Kg/s of heated oil at 175 ºC. The process operates continuously for 12 hours per day, 360 days per year and design analysis can be taken as steady state conditions. The oil is at an inlet pressure of 2.5 bars and exits at a pressure of 24.89 bars. The oil can be treated as an incompressible liquid with a specific heat, c, of 2342 J/(Kg K) and a density of 789 Kg/m3. The device of interest is the boiler/heat exchanger used to heat the oil from an inlet temperature of Tin = 25 ºC. The device is heavily insulated and the total thermal resistance between it and the surroundings is RT = 0.32 K/W for heat transfer calculations. The surroundings are at 25 ºC. For heat transfer process the temperature of the heater is at its average temperature of 100 C, the average temperature. The surroundings can be considered to be the dead state, 298 K and 1 bar.
The current boiler/heat exchanger device will be retired, and its replacement is under consideration. You have been tasked with investigating the electric heater replacement as described above.
The replacement electrically heated boiler/heat exchanger has the following characteristics. The electricity in your region is produced using #2 fuel oil (C12H24) in an old plant with an efficiency of 29%.The heating value of the fuel is 40.6 MJ/Kg and its exergy is 32.53 MJ/Kg (note this is on a mass basis) The installed cost of the boiler is $30,000 and it has an expected lifetime of 20 years. The yearly cost to operate and maintain the boiler is estimated at $0.003/kWh (note this cost is per output energy load). The cost of the oil entering the device is $1.00/Kg. The cost of electricity is $0.17/kWh and is constant. The plant operator salary and fringe benefits to maintain and operate this device is $43,000 per year. The company would pay for this alternative without borrowing money and interest is neglected. For this alternative determine:
1. [5]The required electrical power to operate the boiler/heat exchanger using the first law energy balance.
2. [6] The rate of exergy destruction produced in the boiler/heat exchanger using the exergy balance.
3. [6] The rate of exergy destruction produced by the utility in producing the required electricity using the exergy balance. The system for this calculation should be the overall utility plant with the fuel input, a heat loss associated with the inefficiency and the electricity produced for this process.
4. [5] Calculate the rate carbon dioxide produced in this process. This requires the use of the reaction equation and consider only the electrical power provided to this device.
5. [5] The second law efficiency of the boiler/heat exchanger.
6. [8] The thermoeconomic cost for the heated oil. NOTE: Thermoeconomic costs are based on a one year time period.
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      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (150μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheMissed (208μs)
      • Illuminate\Database\Events\StatementPrepared (1.03ms)
      • Illuminate\Database\Events\QueryExecuted (942μs)
      • eloquent.retrieved: App\Models\SubjectCat (66μs)
      • Illuminate\Cache\Events\KeyWritten (1.13ms)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (304μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (138μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (325μs)
      • Illuminate\Cache\Events\CacheHit (484μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • creating: site.layouts.app (347μs)
      • composing: site.layouts.app (69μs)
      • creating: components.canonical (421μs)
      • composing: components.canonical (81μs)
      • creating: components.open-graph (143μs)
      • composing: components.open-graph (48μs)
      • creating: site.headers.header (258μs)
      • composing: site.headers.header (59μs)
      • Illuminate\Cache\Events\CacheHit (1.38ms)
      • creating: components.footer (74μs)
      • composing: components.footer (68μs)
      • Illuminate\Cache\Events\CacheHit (638μs)
      • Illuminate\Cache\Events\CacheMissed (246μs)
      • Illuminate\Database\Events\StatementPrepared (738μs)
      • Illuminate\Database\Events\QueryExecuted (1.36ms)
      • eloquent.retrieved: App\Models\SubjectCat (84μs)
      • Illuminate\Cache\Events\KeyWritten (324μs)
      • Illuminate\Cache\Events\CacheHit (304μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (253μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • creating: components.forms.contact-us (211μs)
      • composing: components.forms.contact-us (119μs)
      • creating: components.forms.get-started (121μs)
      • composing: components.forms.get-started (46μs)
      • creating: components.forms.free-tool-download (84μs)
      • composing: components.forms.free-tool-download (39μs)
      • creating: components.forms.claim-free-worksheet (92μs)
      • composing: components.forms.claim-free-worksheet (53μs)
      • creating: components.forms.tutor-subscription-waitlist (86μs)
      • composing: components.forms.tutor-subscription-waitlist (39μs)
      • creating: components.forms.tutor-subscription-join (79μs)
      • composing: components.forms.tutor-subscription-join (39μs)
      • creating: components.forms.tutor-support (115μs)
      • composing: components.forms.tutor-support (48μs)
      • 313 x Illuminate\Cache\Events\CacheHit (15.07%)
        65.41ms
        18 x Illuminate\Database\Events\StatementPrepared (6.05%)
        26.24ms
        18 x Illuminate\Database\Events\QueryExecuted (5.21%)
        22.62ms
        9 x Illuminate\Cache\Events\CacheMissed (1.85%)
        8.03ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.31%)
        5.70ms
        9 x Illuminate\Cache\Events\KeyWritten (1.31%)
        5.66ms
        1 x Illuminate\Routing\Events\Routing (0.31%)
        1.35ms
        10 x eloquent.retrieved: App\Models\SubjectCat (0.21%)
        908μs
        1 x Illuminate\Database\Events\ConnectionEstablished (0.21%)
        905μs
        1 x Illuminate\Routing\Events\RouteMatched (0.12%)
        538μs
        1 x creating: components.breadcrumbs (0.12%)
        505μs
        1 x eloquent.booting: App\Models\SubjectCat (0.11%)
        479μs
        1 x creating: components.canonical (0.1%)
        421μs
        1 x creating: site.layouts.app (0.08%)
        347μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.07%)
        284μs
        13 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.06%)
        270μs
        1 x creating: site.headers.header (0.06%)
        258μs
        2 x eloquent.retrieved: App\Models\Subject (0.05%)
        228μs
        1 x creating: components.forms.contact-us (0.05%)
        211μs
        1 x creating: homework.show (0.05%)
        197μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        171μs
        1 x composing: components.breadcrumbs (0.03%)
        150μs
        1 x creating: components.open-graph (0.03%)
        143μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        132μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)
        131μs
        1 x creating: components.forms.get-started (0.03%)
        121μs
        1 x composing: components.forms.contact-us (0.03%)
        119μs
        1 x composing: homework.show (0.03%)
        115μs
        1 x creating: components.forms.tutor-support (0.03%)
        115μs
        1 x eloquent.booting: App\Models\Subject (0.03%)
        113μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        92μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        86μs
        1 x creating: components.forms.free-tool-download (0.02%)
        84μs
        1 x composing: components.canonical (0.02%)
        81μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        79μs
        1 x creating: components.footer (0.02%)
        74μs
        1 x composing: site.layouts.app (0.02%)
        69μs
        1 x composing: components.footer (0.02%)
        68μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        61μs
        1 x composing: site.headers.header (0.01%)
        59μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        53μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        51μs
        1 x composing: components.open-graph (0.01%)
        48μs
        1 x composing: components.forms.tutor-support (0.01%)
        48μs
        1 x composing: components.forms.get-started (0.01%)
        46μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        43μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        39μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        39μs
        1 x composing: components.forms.free-tool-download (0.01%)
        39μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.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 college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      18 statements were executed, 5 of which were duplicates, 13 unique. Show only duplicated34.53ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '50999' limit 1
        7.2mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 50999
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 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
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (371)
        1.3mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 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
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (50999)
        2.45mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 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
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        930μstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 10
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 50999 and `subject` = 371 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        3.54mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 50999
        • 1: 371
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (371)
        1.12mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 50999 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        870μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50999
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 50999 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        860μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50999
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 50999 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        840μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 50999
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.5mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 10
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.07mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        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` = 3 limit 1
        3.24mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        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` = 10 limit 1
        1.13mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        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` = 33 limit 1
        1.09mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        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` = 11 limit 1
        1.18mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        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` = 5 limit 1
        3.64mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        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` = 31 limit 1
        1.41mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        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` = 36 limit 1
        1.16mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        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
        • 28. view::components.footer:170
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      13HomeworkLibraryFile.php
      App\Models\SubjectCat
      10SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
          v2VIW0btTwO21GcYfcAwFrbiQMRUDCokH5ZiYquk
          utm_source
          direct
          redirectUrl
          /college-homework-library/Engineering/Energy-Systems-Engineering/50999
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Engineering/Ene...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Engineering/Energy-Systems-Engineering/50999
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:21 [ "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "x-amzn-trace-id" => array:1 [ 0 => "Root=1-680e427a-2a60c4785160a493102ab023" ] "host" => array:1 [ 0 => "staging.dev.24houranswers.com" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "18.188.83.180" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
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