211)We only take Pext=nRT/V in reversible process i.e. Pext≈Pint=nRT/V
2)For cont. temp U remains const. only for a closed or isolated process,where there is no change of mass.
For open systems,more no. of molecules at same temp. may be added,this increases the total int. energy.
3)Adiabatic process is a process where heat exchanged is zero.i.e. there is interaction between work done and int. energy.
A simple example of constant pressure adiabatic change is a quick[adiabatic] irreversible expansion against const. external pressure.Here work is done at the cost of int. energy.
The 3rd one is interesting:
Now from 1st law of thermo-d.
Q=U+W [heat supplied=inc. in int. energy+work done]
Work done can be of 2 types:
useful:like electric[nFe]
non-useful:PV work.
Therefore we can rewrite it as:
Q=U+PVwork+Wuseful ....(i)
Note that the statement:
Q=U+PVwork
is wrong,as it does not include all work done.
For Adiabatic process Q=0.
Now,equating E=U+PV & (i)
E=-Wuseful
Hence the result.