3. The entropy of an ideal gas is S = Nkg In V. Entropy is a state function rather than a path function, and in this problem, you will show an example of the entropy change for an ideal gas being the same when you go between the same two states by two different pathways. A. Express ASV = S2 (V2) - S₁(V1), the change in entropy upon changing the volume from V₁to V2, at fixed particle number N and energy, U. B. Express ASN = S₂(N₂) - S₁ (N₁), the change in entropy upon changing the particle number from N₁ to N2, at fixed volume V and energy U. C. Write an expression for the entropy change, AS, for a two-step process (V₁, N₁) → (V2, N₁) → (V2, N₂) in which the volume changes first at fixed particle number, then the particle number changes at fixed volume. Again, assume energy is constant.

Please don't use Chatgpt will upvote and give handwritten solution

6. We used the constant volume heat capacity, Cv, when we talked about thermodynamic cycles. It acts as a proportionality constant between energy and temperature: dU = C₁dT. You can also define a heat capacity for constant pressure processes, Cp. You can think of enthalpy playing a similar role to energy, but for constant pressure processes δαρ C = (37) - Sup Ср ат P = ат Starting from the definition of enthalpy, H = U + PV, find the relationship between Cy and Cp for an ideal gas.