.. _sphx_glr_api_gallery_thermodynamics_laws:

Laws
----

The first law (energy is conserved) and the second (entropy never decreases).


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="James Prescott Joule spent the 1840s showing that a given amount of work, however it is done, always produces the same amount of heat. In his best known experiment (published 1850) falling weights turned a paddle wheel in an insulated can of water, and he measured the temperature rise to a hundredth of a degree. His result, 772 foot-pounds per British thermal unit, made heat and work two forms of one conserved quantity, energy: Q = \Delta U + W (~engineeringkit.thermodynamics.first_law_heat). The example redoes the paddle-wheel balance, converts Joule&#x27;s number to SI, and checks the ideal-gas energy functions.">

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  .. image:: /api/gallery/thermodynamics/laws/images/thumb/sphx_glr_plot_01_joule_first_law_thumb.png
    :alt:

  :doc:`/api/gallery/thermodynamics/laws/plot_01_joule_first_law`

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      <div class="sphx-glr-thumbnail-title">Joule and the first law (1843-1850)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Rudolf Clausius (1854) showed that around any cycle the heat received, each part divided by the temperature at which it crosses the boundary, sums to zero or less: \oint \delta Q/T \le 0 (~engineeringkit.thermodynamics.clausius_inequality), with equality only for a reversible cycle. Then \delta Q_{rev}/T is the change of a state function, which in 1865 he named entropy. The example builds a Carnot cycle from an ideal gas, checks that its Clausius sum is zero, and shows that drawing the same heat across a finite temperature difference makes the sum negative.">

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  .. image:: /api/gallery/thermodynamics/laws/images/thumb/sphx_glr_plot_02_clausius_entropy_thumb.png
    :alt:

  :doc:`/api/gallery/thermodynamics/laws/plot_02_clausius_entropy`

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      <div class="sphx-glr-thumbnail-title">Clausius's inequality and entropy (1854-1865)</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/thermodynamics/laws/plot_01_joule_first_law
   /api/gallery/thermodynamics/laws/plot_02_clausius_entropy