Question

To find △H by considering a reversible adiabatic process where Initial conditions are P1,V1 and T1 and final variables are P2,T2,V2 also it implies pvγ=k hence △U=P2V2−P1V1/γ−1, △(PV)=P2V2−P1V1 and since △H = △U + △(PV), △H=γ(P2V2−P1V1)/γ−1

What is wrong with this proof?

Answer 1

The incorrect proof offered by the student for calculating the change in enthalpy ΔH in an adiabatic process stems from incorrectly derived formulas for change in internal energy ΔU and Δ(PV), not adhering to the principles of adiabatic processes relating to specific heats and the gamma exponent.

Step-by-step explanation:

The student has asked about a discrepancy in calculating the change in enthalpy ΔH for an adiabatic process using the equations given. The error lies in the application of the formula for the change in internal energy ΔU in relation to the enthalpy change ΔH.

Specifically, they have used the wrong equation for ΔU. The correct approach to determine ΔU for an adiabatic process involves the specific heats, not the pressure and volume directly. Additionally, the equation for Δ(PV) does not correctly derive from the relation of pressure and volume for an adiabatic process, as it disregards the gamma (γ) exponent.

Therefore, the formula ΔH = γ(P2V2 − P1V1)/(γ − 1) is incorrect because it stems from fundamental misunderstandings of the relations between the variables in an adiabatic process.