thermo memorization

dU = ?

dU = ?

TdS - PdV

dH = ?

TdS + VdP

dA = ?

-SdT - PdV

dG = ?

-SdT + VdP

(dU/dV)S

-P

(dH/dS)p

T

(dH/dP)s

V

(dA/dT)v

-S

(dA/dV)T

-P

(dG/dT)P

-S

(dG/dP)T

V

Maxwell relation: (dT/dV)S

-(dP/dS)V

Maxwell relation: (dT/dP)S

(dV/dS)P

Maxwell relation: (dS/dV)T

(dP/dT)V

Maxwell relation: (dS/dP)T

-(dV/dT)P

(dU/dT)V

Cv

(dH/dT)P

Cp

(dP/dT)V

α/K_T

(dP/dV)T

(bulk modulus) = -1/VK_T

(dS/dT)V

Cv/T

(dS/dT)P

Cp/T

α_v

1/V * (dV/dT)P

K_T

-1/V * (dV/dP)T

avogadros number

6.023 × 10²³

Chain Rule (changes variable being differentiated w respect to)

(dz/dw)x = (dz/dy)x(dy/dw)x

Generalized Chain Rule (want different constant condition)

(dz/dx)w = (dz/dx)y + (dz/dy)x(dy/dx)w

Triplet Rule (promote constant condition to function)

(dy/dx)z = -(dz/dx)y/(dz/dy)x

Independence of Differentiation Order (maxwell’s relationship)

(d²z/dxdy) = d/dx[(dz/dy)x]y = d/dy[(dz/dx)y]x

when is δQ positive?

energy (heat) entering the system by thermal conduction from the environment

when is δW positive?

the system does work on the environment; energy is being extracted across the boundary of the system