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চাপীয় সূত্র

একাদশ- দ্বাদশ শ্রেণি - পদার্থবিদ্যা পদার্থবিজ্ঞান – ১ম পত্র | - | NCTB BOOK

এ সূত্রের সাহায্যে স্থির আয়তনে গ্যাসের চাপ ও তাপমাত্রার মধ্যে সম্পর্ক পাওয়া যায় ।

সূত্র : স্থির আয়তনে কোনো নির্দিষ্ট ভরের গ্যাসের চাপ 0°C থেকে প্রতি ডিগ্রি সেলসিয়াস তাপমাত্রা বৃদ্ধি বা 1 হ্রাসের জন্য এর 0°C তাপমাত্রার চাপের 1273অংশ যথাক্রমে বৃদ্ধি বা হ্রাস পায়।

এ নির্দিষ্ট ভগ্নাংশ 1273 হচ্ছে স্থির আয়তনে গ্যাসের চাপ প্রসারণ সহগ। এটি নির্দেশ করে স্থির আয়তনে 0°C তাপমাত্রার নির্দিষ্ট ভরের গ্যাসের তাপমাত্রা 0°C থেকে প্রতি ডিগ্রি সেলসিয়াস বৃদ্ধি করলে ঐ গ্যাসের প্রতি একক চাপে চাপের কতটুকু বৃদ্ধি ঘটে। একে γν দিয়ে সূচিত করা হয়।

   চাপের সূত্রানুসারে স্থির আয়তনে কোনো নির্দিষ্ট ভরের গ্যাসের চাপ 0°C তাপমাত্রায় po হলে 0°C থেকে প্রতি ডিগ্রি সেলসিয়াস তাপমাত্রা পরিবর্তনের জন্য এর চাপ   1273X P° হারে পরিবর্তিত হবে।  θ°C তাপমাত্রা পরিবর্তনের জন্য চাপের

পরিবর্তন হবে θ273 P° । সুতরাং    θ°C তাপমাত্রায় ঐ গ্যাসের চাপ যদি p হয় তবে চাপীয় সূত্রানুসারে,

 

এখানে T' হচ্ছে θ°C তাপমাত্রার আনুষঙ্গিক পরম বা কেলভিন তাপমাত্রা। যেহেতু Po273 একটি ধ্রুব রাশি সুতরাং

pT যখন আয়তন ও ভর স্থির থাকে।

অতএব চাপের সূত্রকে লেখা যায়,

স্থির আয়তনে নির্দিষ্ট ভরের গ্যাসের চাপ এর পরম বা কেলভিন তাপমাত্রার সমানুপাতিক। 

 অর্থাৎ গ্যাসের ভর ও আয়তন স্থির রেখে কেলভিন তাপমাত্রা দ্বিগুণ করা হলে চাপ দ্বিগুণ হবে, কেলভিন তাপমাত্রা তিনগুণ করা হলে চাপ তিন গুণ হবে।

common.content_added_and_updated_by

# বহুনির্বাচনী প্রশ্ন

টপ রেটেড অ্যাপ

স্যাট অ্যাকাডেমী অ্যাপ

আমাদের অল-ইন-ওয়ান মোবাইল অ্যাপের মাধ্যমে সীমাহীন শেখার সুযোগ উপভোগ করুন।

ভিডিও
লাইভ ক্লাস
এক্সাম
ডাউনলোড করুন
Promotion
Request history8.2.27PHP Version174msRequest Duration38MBMemory UsageGET academy/{slug}Route
    • Booting (103ms)time
    • Application (70.76ms)time
    • 1 x Booting (59.34%)
      103ms
      1 x Application (40.66%)
      70.76ms
      113 templates were rendered
      • 1x academy.subject.read_chapterread_chapter.blade.php#?blade
      • 1x academy.include.sidebarListsidebarList.blade.php#?blade
      • 1x academy.include.left_sidebar_menuleft_sidebar_menu.blade.php#?blade
      • 70x academy.include.sidebarSubListsidebarSubList.blade.php#?blade
      • 5x academy.include.question_cardquestion_card.blade.php#?blade
      • 1x common.modal.self_test_modalself_test_modal.blade.php#?blade
      • 1x common.modal.bookmark_modalbookmark_modal.blade.php#?blade
      • 1x common.modal.error_report_modalerror_report_modal.blade.php#?blade
      • 1x common.modal.video_modalvideo_modal.blade.php#?blade
      • 1x common.script.page_type_scriptpage_type_script.blade.php#?blade
      • 1x job.job_include.job_scriptjob_script.blade.php#?blade
      • 1x common.script.activity_scriptactivity_script.blade.php#?blade
      • 1x common.script.test_scripttest_script.blade.php#?blade
      • 1x common.script.custom_dropdowncustom_dropdown.blade.php#?blade
      • 1x common.script.follow_unfollow_scriptfollow_unfollow_script.blade.php#?blade
      • 1x common.script.short_statistics_scriptshort_statistics_script.blade.php#?blade
      • 1x common.script.navigator_sharenavigator_share.blade.php#?blade
      • 1x layouts.satt-appsatt-app.blade.php#?blade
      • 1x includes.header_link2header_link2.blade.php#?blade
      • 1x laravelpwa::metameta.blade.php#?blade
      • 1x layouts.headerheader.blade.php#?blade
      • 1x layouts.toolbartoolbar.blade.php#?blade
      • 1x frontend.downloadourappdownloadourapp.blade.php#?blade
      • 1x frontend.referralreferral.blade.php#?blade
      • 1x auth.user_type_modaluser_type_modal.blade.php#?blade
      • 1x layouts.footerfooter.blade.php#?blade
      • 1x common.login_modallogin_modal.blade.php#?blade
      • 1x components.authentication-card-logoauthentication-card-logo.blade.php#?blade
      • 1x common.includes.promotion_modalpromotion_modal.blade.php#?blade
      • 1x common.includes.notification_item_modalnotification_item_modal.blade.php#?blade
      • 1x common.includes.notification_item_list_modalnotification_item_list_modal.blade.php#?blade
      • 1x common.includes.promotion_offcanvaspromotion_offcanvas.blade.php#?blade
      • 1x includes.footer_link2footer_link2.blade.php#?blade
      • 1x includes.restrictrestrict.blade.php#?blade
      • 1x livewire-alert::components.scriptsscripts.blade.php#?blade
      • 1x livewire-alert::components.flashflash.blade.php#?blade
      • 1x admin.include.toastrtoastr.blade.php#?blade
      • 1x common.search.search_scriptsearch_script.blade.php#?blade
      • 1x common.script.promotion_scriptpromotion_script.blade.php#?blade
      • 1x common.script.promotion_functionspromotion_functions.blade.php#?blade
      uri
      GET academy/{slug}
      middleware
      web, throttle:global
      controller
      App\Http\Controllers\Academy\SubjectController@chapter
      namespace
      prefix
      where
      as
      academy.subject.chapter
      file
      app/Http/Controllers/Academy/SubjectController.php:102-110
      22 statements were executed (4 duplicates)Show only duplicates27.26ms
      • SubjectService.php#34debugerror_satt600μsupdate `subjects` set `view_count` = `view_count` + 1, `subjects`.`updated_at` = '2025-03-13 11:12:39' where `id` = 2346
        Bindings
        • 0: 2025-03-13 11:12:39
        • 1: 2346
        Backtrace
        • app/Services/SubjectService.php:34
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
        • vendor/laravel/framework/src/Illuminate/Routing/Route.php:266
      • QueryBuilder.php#38debugerror_satt160μsselect `_lft`, `_rgt` from `subjects` where `id` = 2346 limit 1
        Bindings
        • 0: 2346
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:38
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:60
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:235
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:227
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
      • QueryBuilder.php#305debugerror_satt240μsselect `id`, `name`, `parent_id`, `_lft`, `_rgt`, `show_content`, `num_of_mcq`, `num_of_written`, `des_added_by`, `des_updated_by`, `author_name`, `link_subject_id`, `sub_category_id`, `main_category_id`, `slug`, `meta_og_title`, `meta_keyword`, `meta_description`, `vote`, `view_count`, `icon`, `page_type`, `chapter_name` from `subjects` where (`subjects`.`_lft` between 14776 and 14777) and `subjects`.`deleted_at` is null
        Bindings
        • 0: 14776
        • 1: 14777
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt210μsselect `id`, `description`, `short_description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (2346) and `subject_descriptions`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt150μsselect `id`, `name`, `avatar` from `users` where `users`.`id` in (40961) and `users`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt110μsselect `id`, `name`, `avatar` from `users` where `users`.`id` in (40961) and `users`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt140μsselect `id`, `name`, `slug` from `sub_categories` where `sub_categories`.`id` in (4878) and `sub_categories`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt170μsselect `id`, `user_id`, `completeable_type`, `completeable_id`, `complete_progress`, `is_complete` from `completes` where `completes`.`completeable_id` in (2346) and `completes`.`completeable_type` = 'App\\Models\\Subject'
        Bindings
        • 0: App\Models\Subject
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt1.27msselect * from (select `questions`.`id`, `questions`.`subject_id`, `questions`.`category_id`, `questions`.`sub_category_id`, `questions`.`board_exam_id`, `questions`.`passage_id`, `questions`.`question_type`, `questions`.`question`, `questions`.`is_duplicate`, `questions`.`status`, `questions`.`image`, `subjectables`.`subject_id` as `pivot_subject_id`, `subjectables`.`subjectable_id` as `pivot_subjectable_id`, `subjectables`.`subjectable_type` as `pivot_subjectable_type`, row_number() over (partition by `subjectables`.`subject_id` order by `questions`.`created_at` desc) as `laravel_row` from `questions` inner join `subjectables` on `questions`.`id` = `subjectables`.`subjectable_id` where `subjectables`.`subject_id` in (2346) and `subjectables`.`subjectable_type` = 'App\\Models\\Question' and `questions`.`status` = 'active' and `questions`.`deleted_at` is null) as `laravel_table` where `laravel_row` <= 5 order by `laravel_row`
        Bindings
        • 0: App\Models\Question
        • 1: active
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt250μsselect `id`, `question_id`, `option_1`, `option_2`, `option_3`, `option_4`, `option_5`, `image_option`, `image_question`, `answer` from `question_options` where `question_options`.`question_id` in (99323, 192383, 231730, 240654, 244989) and `question_options`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt120μsselect `id`, `name`, `slug` from `subjects` where `subjects`.`id` in (75) and `subjects`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt210μsselect `subjects`.`id`, `subjects`.`name`, `subjects`.`slug`, `subjectables`.`subjectable_id` as `pivot_subjectable_id`, `subjectables`.`subject_id` as `pivot_subject_id`, `subjectables`.`subjectable_type` as `pivot_subjectable_type`, `subjectables`.`created_user_id` as `pivot_created_user_id`, `subjectables`.`deleted_at` as `pivot_deleted_at`, `subjectables`.`status` as `pivot_status`, `subjectables`.`created_at` as `pivot_created_at`, `subjectables`.`updated_at` as `pivot_updated_at` from `subjects` inner join `subjectables` on `subjects`.`id` = `subjectables`.`subject_id` where `subjectables`.`subjectable_id` in (99323, 192383, 231730, 240654, 244989) and `subjectables`.`subjectable_type` = 'App\\Models\\Question' and `subjects`.`deleted_at` is null
        Bindings
        • 0: App\Models\Question
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • QueryBuilder.php#305debugerror_satt120μsselect `id`, `title`, `passage` from `passages` where `passages`.`id` in (0) and `passages`.`deleted_at` is null
        Backtrace
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:305
        • vendor/kalnoy/nestedset/src/QueryBuilder.php:321
        • app/Repositories/SubjectRepository.php:280
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
      • SubjectRepository.php#117debugerror_satt170μsselect * from `subjects` where `subjects`.`id` = 2346 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 2346
        Backtrace
        • app/Repositories/SubjectRepository.php:117
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:116
        • app/Services/SubjectService.php:51
      • SubjectRepository.php#120debugerror_satt8.68msselect `id`, `name`, `slug`, `parent_id`, `_lft`, `_rgt` from `subjects` where (14777 between `subjects`.`_lft` and `subjects`.`_rgt` and `subjects`.`id` <> 2346) and `subjects`.`deleted_at` is null order by `_lft` asc
        Bindings
        • 0: 14777
        • 1: 2346
        Backtrace
        • app/Repositories/SubjectRepository.php:120
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:116
        • app/Services/SubjectService.php:51
      • SubjectRepository.php#132debugerror_satt170μsselect * from `subjects` where `subjects`.`id` = 2346 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 2346
        Backtrace
        • app/Repositories/SubjectRepository.php:132
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:131
        • app/Services/SubjectService.php:52
      • SubjectRepository.php#135debugerror_satt130μsselect `id`, `name`, `parent_id`, `_lft`, `_rgt`, `slug`, `meta_og_title`, `meta_keyword`, `meta_description` from `subjects` where `subjects`.`id` = 2243 and `subjects`.`deleted_at` is null limit 1
        Bindings
        • 0: 2243
        Backtrace
        • app/Repositories/SubjectRepository.php:135
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:131
        • app/Services/SubjectService.php:52
      • SubjectRepository.php#135debugerror_satt130μsselect `id`, `description`, `subject_id` from `subject_descriptions` where `subject_descriptions`.`subject_id` in (2243) and `subject_descriptions`.`deleted_at` is null
        Backtrace
        • app/Repositories/SubjectRepository.php:135
        • vendor/laravel/framework/src/Illuminate/Cache/Repository.php:427
        • vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:453
        • app/Repositories/SubjectRepository.php:131
        • app/Services/SubjectService.php:52
      • SubjectRepository.php#320debugerror_satt170μsselect * from `mediables` where `mediable_type` = 'App\\Models\\Subject' and `mediable_id` in (2346)
        Bindings
        • 0: App\Models\Subject
        • 1: 2346
        Backtrace
        • app/Repositories/SubjectRepository.php:320
        • app/Services/SubjectService.php:67
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
      • SubjectRepository.php#335debugerror_satt140μsselect `videos`.`video_src_url`, `mediables`.`mediable_id` as `chapter_id` from `videos` inner join `mediables` on `mediables`.`mediable_id` = `videos`.`id` where `videos`.`id` = 0 and `videos`.`video_src` = 'youtube' and `videos`.`deleted_at` is null
        Bindings
        • 0: 0
        • 1: youtube
        Backtrace
        • app/Repositories/SubjectRepository.php:335
        • app/Services/SubjectService.php:68
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
      • SubjectService.php#73debugerror_satt13.73msselect `id`, `name`, `main_category_id`, `slug` from `subjects` where `id` <> 2346 and `parent_id` = 2243 and `main_category_id` = 2 and `subjects`.`deleted_at` is null limit 5
        Bindings
        • 0: 2346
        • 1: 2243
        • 2: 2
        Backtrace
        • app/Services/SubjectService.php:73
        • app/Http/Controllers/Academy/SubjectController.php:105
        • vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:44
        • vendor/laravel/framework/src/Illuminate/Routing/Route.php:266
      • restrict.blade.php#30debugerror_satt190μsselect * from `package_plans` where `status` = 'active' and `package_plans`.`deleted_at` is null
        Bindings
        • 0: active
        Backtrace
        • view::includes.restrict:30
        • vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
        • vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • vendor/livewire/livewire/src/Mechanisms/ExtendBlade/ExtendedCompilerEngine.php:22
        • vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:75
      App\Models\Subject
      18Subject.php#?
      App\Models\Question
      5Question.php#?
      App\Models\QuestionOption
      5QuestionOption.php#?
      App\Models\PackagePlan
      4PackagePlan.php#?
      App\Models\SubjectDescription
      2SubjectDescription.php#?
      App\Models\User
      2User.php#?
      App\Models\SubCategory
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