Equations

Question 1

1st Law?

Answer 1

Delta U = q + w

Question 2

2nd Law?

Answer 2

delta s = q(rev)/T

Question 3

Equation for enthalpy?

Answer 3

H = U + PV

Question 4

constant volume Heat capacity?

Answer 4

Cv = Delta U/delta T

Question 5

Constant pressure heat capacity?

Answer 5

Cp = delta H/delta T

Question 6

Claperyon equation?

Answer 6

dP/dT = delta S/delta V

Question 7

How do you derive the Claperyon equation?

Answer 7

• equilibrium mean Gvap = Gliq
• consider a small change of G (dG)
• dG = dH - SdT -TdS
• use 1st and 2nd law –> dU = TdS - PdV
• and dH = dU + VdP
• Therefore, dG = VdP - SdT
• using this equal dGliq = dGvap
• Therefore dP/dT = delta S/delta V

Question 8

How do you derive Claus-Claperyon equation?

Answer 8

• assume volume of liquid is negligible compared to volume of vapour
• assume vapour behaves as an ideal gas
• Therefore, Delta V = Vvap - Vliq = Vvap
• Vvap = RT/P for 1 mole (PV = nRT)
• delta G = 0 (at equil G = min)
• Therefore, delta S= delta H/T
• sub into claperyon –> dP/dT = (Delta H x P)/RT^2
• Separate and integrate
• ln(P) = -(delta H)/RT + C