Question

for a van der waals gas, phi (At constant T)= a / Vmolar^2. calculate change of U molar for the isothermal reversible expansion of Nitrogen gas from an initial Volume of 1 L to 24.8 L at 298 K.what are the values of q and w?

Answer 1

FIgured it out. Using\[dU = (dU/dT)_{V}dT+(dU/dV)_{T}dV\] We know that this is isothermic, so change in T=0, which means we're left with the change in internal energy is equal to phi at constant t (which is given) integrated from Vf to Vi with respect to V. Then work can be calculated using w=p(V)dV, with the van der waals eqn subbed in for p(V) and integrated from Vf to Vi.
Finally, heat can be calculated because work and change in U are known, since change in U=q+w.