THM-09

First law of thermodynamics

ΔU = Q − W. Heat in minus work out raises the internal energy.

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First lawFirst law

Governing equation

\Delta U=Q-W

$Q \in \left[-200, 400\right]$

where

Q: Heat in (kJ)
W: Work out (kJ)
\Delta U: Internal energy change (kJ)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\Delta U=Q-W

$Q \in \left[-200, 400\right]$

$Q = -200$ $\Delta U = -220$

Along the curve

②

Domain of the variable — blue

Q_{\min} = -200,\quad Q_{\max} = 400

$Q \in \left[-200, 400\right]$

$Q = -200$ $Q = -200$

Along the curve

③

Response curve — green

\Delta U=Q-W

$Q \in \left[-200, 400\right]$

$Q = -200$ $\Delta U = -220$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta U}{\mathrm{d}Q}

$Q \in \left[-200, 400\right]$

$Q = -196.2$ $\Delta U^{\prime} = 1$

Along the curve

Lecture brief

Historical brief

Carnot (1824), Clausius entropy, the first law and later van der Waals and Gibbs potentials turned heat into a state science. The sheets compute work, efficiency and vapour pressure. This sheet (THM-09 — First law of thermodynamics) is the form associated with First law. Working symbols: $Q$ , $W$ $\rightarrow$ $\Delta U$ . Sign convention: W is work done by the system (chemistry/engineering). Physics often flips W.

Purpose

Purpose: compute

\Delta U

from

Q

W

in Thermodynamics via

\Delta U=Q-W

ΔU = Q − W. Heat in minus work out raises the internal energy. Use it when a real thermodynamics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Q = 50.000\,\mathrm{kJ}

W = 20.000\,\mathrm{kJ}

, the governing relation

\Delta U=Q-W

yields

\Delta U = 30.00\,\mathrm{kJ}

. A piston, a heat arrow, an internal-energy well. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Heat in Q50 kJWork out W20 kJ

Outputs

Internal energy change \Delta U30.00 kJ

Reading speed

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Narration of this film

A piston, a heat arrow, an internal-energy well.

Sign convention: W is work done by the system (chemistry/engineering). Physics often flips W.

Reading speed

Watch on YouTube