[ZHR]

1))Why DU=CvdT for ideal gases even if the volume isnt constant?
2))Why DH=CpdT for ideal gases even if the pressure isnt constant?

3))Joule–Thomson effect I didnt manage to understand properly the mathmathics behind those equasions if someone can help me with that I'd really apprieciate, thanks.

[mjc123]

Because you are dealing with state functions, the path doesn't matter. You can always get from initial (P1, V1, T1) to final (P2, V2, T2) state by a combination of a constant volume (or pressure) step and an isothermal step. For ideal gases, ΔU = 0 for the isothermal step. So for example
Constant vol: P1, V1, T1  P3, V1, T2   ΔU = C_vΔT
Isothermal: P3, V1, T2  P2, V2, T2   ΔU = 0

Constant pressure: P1, V1, T1  P1, V3, T2   ΔH = C_pΔT
Isothermal: P1, V3, T2  P2, V2, T2   ΔH = ΔU + Δ(PV) = 0

[mjc123]

Don't edit your post to ask a fresh question. Make a new post.

What is it you don't understand about the maths? It looks pretty straightforward. Are you familiar with algebraic rearrangement of equations? (We do get people sometimes who don't realise that if a = b/c, then c = b/a.) Otherwise, what's the problem?

[ZHR]

Thanks for the help.
and my fault about the equasion i was confused