{"id":838,"date":"2026-08-20T19:37:51","date_gmt":"2026-08-20T19:37:51","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=838"},"modified":"2026-08-24T13:03:37","modified_gmt":"2026-08-24T13:03:37","slug":"first-law-of-thermodynamics","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/thermodynamics\/first-law-of-thermodynamics\/","title":{"rendered":"The First Law of Thermodynamics"},"content":{"rendered":"\n
Definition<\/div>

\n\nThe first law of thermodynamics states that the change in a system’s internal energy equals the heat added to the system minus the work done by the system: \u0394U = Q \u2212 W. It is the law of conservation of energy applied to thermodynamic processes, meaning energy can change form \u2014 from heat to work or internal energy \u2014 but can never be created or destroyed.\n\n<\/p><\/div>\n\n

Every time you rub your hands together on a cold morning, you convert mechanical work into thermal energy \u2014 and your palms warm up. That warmth did not appear from nothing. It came from the effort your muscles supplied, following a rule that the universe enforces without exception.<\/p>

That rule is the first law of thermodynamics. It keeps track of every joule entering or leaving a system, and it guarantees that the books always balance. Understanding it unlocks the physics behind engines, refrigerators, weather, and your own metabolism.<\/p>

What Is the First Law of Thermodynamics?<\/h2>

The first law of thermodynamics is the law of conservation of energy applied to systems that exchange heat and work with their surroundings. It says that when you add heat to a system or do work on it, the total energy the system gains must equal the total energy it receives \u2014 no more, no less.<\/p>

Think of a sealed container of gas sitting on a hotplate. You supply heat (Q) to the gas. Some of that energy makes the gas molecules jiggle faster, raising the temperature \u2014 what physicists call internal energy<\/a>. Some of it may push a piston outward, doing work (W) on the surroundings. The first law simply insists that these two portions add up to the heat you put in.<\/p>

In other words, energy has only three places to go in a thermodynamic process: into internal energy, out as work, or in as heat. The first law is the accountant that tracks every transfer.<\/p>

This idea was not always obvious. Before the 1840s, scientists treated heat and mechanical work as separate, unrelated quantities. It took the careful experiments of James Prescott Joule \u2014 who measured the temperature rise of water churned by falling weights \u2014 to prove that work and heat are interchangeable forms of the same thing: energy<\/a>. NASA’s Glenn Research Center offers a clear walkthrough<\/a> of how Joule’s insight led to the modern definition of internal energy.<\/p>

The First Law of Thermodynamics Formula<\/h2>

The first law of thermodynamics is written as:<\/p>\n\n

\u0394U = Q \u2212 W<\/div>\n\n

where:<\/p>

  • \u0394U<\/strong> = change in internal energy of the system (joules, J)<\/li>
  • Q<\/strong> = heat added to the system (joules, J)<\/li>
  • W<\/strong> = work done by<\/em> the system on its surroundings (joules, J)<\/li> <\/ul>

    Sign conventions<\/h3>

    Getting the signs right trips up more students than the formula itself. Here is the convention used in most physics courses (the “physics” sign convention):<\/p>

    Quantity<\/th> Positive (+)<\/th> Negative (\u2212)<\/th> <\/tr> <\/thead>
    Q (heat)<\/strong><\/td> Heat flows into<\/em> the system<\/td> Heat flows out of<\/em> the system<\/td> <\/tr>
    W (work)<\/strong><\/td> System does work on<\/em> surroundings (expansion)<\/td> Surroundings do work on<\/em> system (compression)<\/td> <\/tr>
    \u0394U<\/strong><\/td> Internal energy increases (system heats up)<\/td> Internal energy decreases (system cools down)<\/td> <\/tr> <\/tbody> <\/table> <\/div>

    A common alternative in chemistry and some engineering texts writes the law as \u0394U = Q + W, where W is defined as work done on<\/em> the system. Both forms say the same thing \u2014 just watch which sign convention the question uses.<\/p>

    What is internal energy?<\/h3>

    Internal energy (U) is the total microscopic energy stored inside a system. For a gas, it includes the kinetic energy of every randomly moving molecule plus the potential energy from intermolecular forces. You cannot measure U directly, but you can measure changes<\/em> in U \u2014 which is exactly what the first law does.<\/p>

    For an ideal gas, internal energy depends only on temperature. Double the absolute temperature and you double U (for a monatomic ideal gas, U = 3<\/sup>\u20442<\/sub> nRT). That link between temperature and internal energy is why heating a sealed gas raises its temperature \u2014 all the added energy stays inside.<\/p>\n\n

    <\/span>First Law of Thermodynamics Lab<\/span><\/div>
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