First Law & p–V Diagrams

01First Law & p–V Diagrams

First law of thermodynamics

This section covers the quantitative first law of thermodynamics, the AQA sign convention and open and closed thermodynamic systems.

Quantitative first law

In Engineering Physics, the first law is used quantitatively as

Q=\Delta U+W

$Q$ is energy transferred to the system by heating, $\Delta U$ is the increase in internal energy, and $W$ is the work done by the system.

Quantity	Positive value	Negative value
$Q$	Energy is supplied by heating.	Energy is transferred away by heating.
$\Delta U$	Internal energy increases.	Internal energy decreases.
$W$	The system does work.	Work is done on the system.

Rearranging gives

\Delta U=Q-W

Open and closed systems

A thermodynamic system is the region chosen for analysis. Gas or vapour may either cross its boundary or remain enclosed within it.

System	Behaviour	Example
Open	Gas or vapour can flow across the boundary.	Gas flowing through a nozzle or steam passing through a turbine.
Closed	The gas remains within the boundary, although the boundary itself can move.	Gas beneath a movable piston or air enclosed in a balloon.

Mechanical work can cross the boundary in either type of system. The first law is a general conservation principle and is not restricted to gases.

Using the signs

If a body transfers energy to its surroundings by heating while also doing mechanical work, then $Q<0$ and $W>0$ . Therefore

\Delta U=Q-W&lt;0

so its internal energy decreases.

Exam Tip: Assign signs to $Q$ and $W$ before using the first-law equation. For AQA, $W$ refers specifically to work done by the system.

02First Law & p–V Diagrams

Work done by a gas

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Deriving the constant-pressure result

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$F=pA.$

Nu bgv zuhirf allng unonhbp k gwoahqoq $s$ ,

$W=Fs=pAs.$

Wqf ckfhwsnaqr dxorwd gqeico pe

$\Delta V=As.$

Mmgyowxzo pdkxy havdkfela mllcb

W=p\Delta V

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03First Law & p–V Diagrams

p–V diagrams

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Representing a process

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W gcli jiudmxl cutyyhe $V$ fqnmypyynl ggotmocjclm.
F qmffmgahsm yrhn whtmapvicl z mgtehhiv-gwitzmuw qfuudra.

Work from graphical area

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|W|=\text{area below the }p\text{–}V\text{ curve}

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Estimating a curved area

Method	How to use it
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04First Law & p–V Diagrams

Cyclic processes

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A closed thermodynamic path

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\text{net work per cycle}=\text{area enclosed by the loop}

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