11.5.2 Isobaric

Isobaric literally means constant pressure. On the P-V diagram, an isobaric expansion is represented by a rightward horizontal line.

If we overlay the isotherms onto the P-V diagram, it is obvious that the gas will be at a higher temperature after an isobaric expansion, since a rightward horizontal line must end at a higher isotherm. A higher temperature means that $\displaystyle \Delta U>0$ .

The gas expanded, so work is done by the gas and $\displaystyle {{W}_{{ON}}}<0$ . Since p is constant, the amount of work during an isobaric process can be calculated very easily using $\displaystyle p\Delta V$ , which corresponds to the rectangular area under the pV graph.

Applying the first law

$\displaystyle \displaystyle \overset{{+ve}}{\mathop{{\Delta U}}}\,=Q+{{\overset{{-ve}}{\mathop{W}}\,}_{{ON}}}$

we can deduce that Q is positive. Conclusion: heat must be supplied to the gas during an isobaric expansion.

A practical example of an isobaric expansion is as follow:

We immerse a cylinder of gas in a hot water bath so that heat is transferred gradually to the gas. If the heating is gradual, the gas will expand slowly. Assuming that the piston is frictionless, the gas will always expand just enough so that the pressure on both sides of the piston are equal. In other words, the heated gas expands at constant pressure of 1 atm.

Concept Test