- #1

fluidistic

Gold Member

- 3,926

- 262

## Homework Statement

Find the relation [itex]P=P(V)[/itex] for a transformation [itex]dQ=0[/itex] in an ideal gas ([itex]PV=nRT[/itex] and [itex]U=CnRT[/itex]).

## Homework Equations

[itex]dU=dQ-PdV[/itex].

## The Attempt at a Solution

If I assume that C and R are constant I get [itex]dU=CR \left [ \frac{\partial (nT)}{\partial n} dn + \frac{\partial (nT)}{\partial T } dT \right ] =-PdV[/itex].

If I assume that n does not depend on T, this simplifies to [itex]dU=CR(Tdn+ndT )=-PdV[/itex]. If I assume that n is constant, dn=0 and so [itex]-PdV=CRndT[/itex]. But since the pressure can depend on the volume, I cannot just integrate this equation. I don't know how to find P(V). Also I think I assumed too many things that weren't stated in the problem statement. Any idea on how to proceed?