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Chemistry Notebook

The first law of thermodynamics

Accounting for heat, work, and changes in internal energy.

An energy balance

Section titled “An energy balance”

For a closed system with negligible changes in kinetic and potential energy, using the chemistry sign convention:

ΔU=q+w.\Delta U=q+w.

Heat entering the system is positive. Work done on the system is positive.

Pressure–volume work

Section titled “Pressure–volume work”

For expansion against a constant external pressure:

w=−Pext(V2−V1).w=-P_{\mathrm{ext}}(V_2-V_1).

An expanding gas has V2>V1V_2>V_1, so this work is negative. The system transfers energy to its surroundings.

A short example

Section titled “A short example”

A gas absorbs 500 J500\,\mathrm{J} of heat and does 200 J200\,\mathrm{J} of work on its surroundings. Then q=+500 Jq=+500\,\mathrm{J} and w=−200 Jw=-200\,\mathrm{J}, giving ΔU=300 J\Delta U=300\,\mathrm{J}.

Check the sign convention

Section titled “Check the sign convention”

Some engineering texts write ΔU=Q−W\Delta U=Q-W, where WW is work done by the system. Both conventions describe the same energy balance. Define your signs before substituting values.