The First Law of Thermodynamics for Any Process
Internal energy changes only by heat added and work done, whatever route the system takes. Applying it means being careful about signs and about which quantities depend on the path.
What a learner can do afterwards
- States the first law with a consistent sign convention and applies it to a stated process
- Explains why internal energy is a state function while heat and work are not
- Traces energy round a complete cycle and shows the internal energy change is zero
1 · Read
The first law says the change in internal energy equals the heat added minus the work done by the system. Energy never appears from nothing. Fix one sign rule, with work by the system counting positive, and keep it for every term.
Internal energy is fixed by the current state alone, so it is a state function. Heat and work describe the route taken, so the same endpoints can pair with many values of each.
Squeeze a gas while it loses heat and two effects fight: the squeeze pushes energy in while the leaking heat drains it, and the change in internal energy is the balance. Heating at fixed volume sends every joule into internal energy, since no boundary work happens, while heating at fixed pressure spends part on work. With no heat flow at all, called adiabatic, any work comes straight from internal energy and the temperature shifts.
Round a full cycle the internal energy change is zero, so the net heat in equals the net work out. Trace each leg with its sign and the loop must balance.
Heat in minus work out sets the change inside, and loops always balance to zero.
More to read
3.3 First Law of Thermodynamics
The first law is energy conservation with bookkeeping. When heat flows into a system, that energy must go somewhere: part of it raises the internal energy and the rest leaves as work the system does on its surroundings. In symbols, the internal energy change equals heat in minus work out. Nothing is created or destroyed, only sorted into two columns.
Signs are where students stumble, so fix one convention and never wobble. Here work done by the system counts positive, which matches the PV diagram picture where expansion area is positive work. Heat entering the system is positive. With that settled, every process becomes an accounting exercise: identify the two known quantities, solve for the third, and check that the signs tell a consistent story.
15.1 The First Law of Thermodynamics
The first law splits state from path. Internal energy cares only about where the system is now: same pressure, volume, and temperature means same internal energy, regardless of the journey. Heat and work care about the journey itself, since a slow gentle expansion and a violent free expansion between the same endpoints involve very different transfers.
Everyday life runs on this law. Your body obeys it when food energy becomes body heat plus muscular work, and a car engine obeys it when fuel energy splits into motion plus waste heat. Whenever someone promises a machine that outputs more than it takes in, the first law is the quiet referee that disallows it.
12.2 First law of Thermodynamics: Thermal Energy and Work
Cycles show the first law at work. Send a working gas round a closed loop and it returns to its exact starting state, so its internal energy change is zero by definition. The first law then collapses to a striking equality: net heat absorbed over the loop equals net work delivered. An engine is nothing but a device that keeps this loop running, skimming off work each lap.
Tracing energy round the loop builds real intuition. On the expansion legs the gas does work and must absorb heat to avoid cooling. On the compression legs work is done on the gas and heat must be dumped. The difference between heat taken in and heat thrown away is the useful output, and the loop area on the PV diagram shows that difference at a glance.
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2 · Watch
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.