Is the Ideal Gas Law Applicable to Non-Isothermal Processes? | Homework Question

[SherlockOhms]

Homework Statement

Is the ideal gas law, PV = mRT, only applicable to processes which are carried out isothermally? I mean, can it not be applied to a polytropic process, PVⁿ = k.

Homework Equations

See above.

The Attempt at a Solution

N.A.

 

[DrClaude]

Is the ideal gas law, PV = mRT, only applicable to processes which are carried out isothermally?

No. It is an equation of state: it relates P, V, and T (assuming n fixed). It is valid everywhere (you can't have an ideal gas at pressure $P_1$ occupying volume $V_1$, and measure temperature $T_1$, and have the same amount of an ideal gas also at $P_1$ and $V_1$ and measure $T_2 \neq T_1$).

For a polytropic process, the equation only tells you what remains constant during the process. In the formulation $PV^\gamma = \text{const.}$, then $T$ must change when $P$ and $V$ change, such that $PV = nRT$ is maintained.

 

[SherlockOhms]

Got it. Thanks for that.