# 11.5.4 Isothermal

Isothermal literally means constant temperature. On the P-V diagram, an isothermal expansion is represented by curve along an isotherm.

Since temperature is constant, $\displaystyle \Delta U=0$ .

Since the gas expanded, $\displaystyle {{W}_{{ON}}}<0$ .

Applying the first law of thermodynamics,

$\displaystyle \displaystyle \overset{0}{\mathop{{\Delta U}}}\,=Q+{{\overset{{\text{-ve}}}{\mathop{W}}\,}_{{ON}}}$

we can deduce that Q is positive, i.e. heat must be supplied to the gas during an isothermal expansion.

A practical example of an isothermal expansion is as follows: We have a cylinder of gas immersed into and at thermal equilibrium with a constant temperature bath. Now draw out the piston of the gas extremely slowly. If it is done slowly enough, heat can flow from the bath to the gas to offset the negative work done on the gas by the retreating piston, so that the temperature of the gas remains constant. It works better if the wall of the cylinder is thin and a good conductor of heat.

Concept Test

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