Question

prove thta delta t + delta u = delta v

Answer 1

volumes in the initial and final states respectively.
For a reaction involving n1​ moles of gaseous reactants in initial state and n2​ moles of gaseous products at final state,
n1​X(g)​→n2​Y(g)​
If H1​ and H2​ are the enthalpies in initial and final states respectively, then the heat of reaction is given by enthalpy change as
ΔH=H2​−H1​
Mathematical definition of 'H' is H=U+PV
Thus, H1​=U1​+P1​V1​ and H2​=U2​+P2​V2​,
∴ΔH=U2​+P2​+P2​V2​−(U1​+P1​V1​)
∴ΔH=U2​+P2​V2​−U1​−P1​V1​
∴ΔH=U2​−U1​+P2​V2​−P1​V1​
Now, ΔU=U2​−U1​
Since, PV=nRT
For initial state, P1​V1​=n1​RT
For final state, P2​V2​=n2​RT
P2​V2​−P1​V1​=n2​RT−n1​RT
=(n2​−n1​)RT
=ΔnRT
where, Δn= [No. of moles of gaseous products] - [No. of moles of gaseous reactants]
∴ΔH=ΔU+ΔnRT
In an isochoric process, the volume remains constant i.e., ΔV=0
Therefore,
ΔH=ΔU