Isochoric, isobaric, isothermal and adiabatic processes

A2

We come across the definitions of these terms at A level:

Iscochoric: at constant volume (or isovolumetric)

Isobaric: at constant pressure

At A2 we take both isothermal and adiabatic to mean at constant temperature.

University

In fact, isothermal means the temperature remains constant, and adiabatic means that there are no heat transfer processes.

All four processes can be presented on a p-V graph (the blue lines are isotherms – lines showing the points at the same temperature):

scan0001

The definitions mean that more is true.

Implications for the first law
Isochoric constant volume dV = 0, so W = pdV = 0 ΔU = Q
Isobaric constant pressure W = pdV = p(V2V1)
Isothermal constant temperature ΔU = 0 Q = W
Adiabatic no heat transfer Q = 0 ΔU = W

Heat capacity for adiabatic processes

From the first law of thermodynamics:

scan0002

Substitute in the definitions of heat capacity and work:

scan0003

scan0004

Rearrange, using the ratio of heat capacities:

scan0006

scan0007

scan0008

Integrate:

scan0010

This also means that:

scan0011

using the ideal gas equation to replace T.

Also from the ideal gas equation we get:

scan0009

These equations are used a lot in Carnot cycles and Otto cycles.

Back to Contents: Physics: Thermodynamics

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s