Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0001 362720 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0840 1212256 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0840 1212256 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.3381 4115736 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.3395 4143512 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.3403 4161224 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.3405 4192256 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.3416 4214976 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.3416 4214976 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.3923 4845896 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.3949 4946880 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.3955 4967808 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.4055 5036752 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.4056 5037008 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

Heat Capacities of Ideal Gases at Constant Volume

For an ideal gas the internal energy depends only on the temperaturewhere

is the number of mols andis the Universal Gas Constant,

When the temperature increases by a small amountthe corresponding change in internal energy is

The specific heat capacity of a substance is defined asso for a gas withmols we see the heat capacity at constant volume isand the molar heat capacity at constant volume, labelledis

In fact the above equation only holds for gases whose particles are single atoms. It is more accurate to say that the molar hear capacity for an ideal gas isper degree of freedom. This allows us to generalise to gases made up of molecules of two or more atoms.

For a monotomic gas there are 3 degrees of freedom: up and down, forwards and backwards, left and right.

For a diatomic gas there are two extra, 'vibrational' degrees of freedom and two extra 'rotational' degrees of freedom, each contributing an extra to the molar heat capacity at constant volume. For a diatomic gas,

It must be noted though that the vibrational degrees of freedom only manifest above certain temperatures. For lower temperatures