Temperature derivative via volume derivative

The Joule—Thompson effect describes the change in temperature that accompanies the expansion of a gas without production of work or transfer of heat, which is in effect an isenthalpic process.

Notes:

1. The left-hand side of the equation is also called the Joule—Thompson coefficient.

Conditions:

1. Particle count is assumed to be constant.

2. Heat capacity is assumed to be independent of temperature.

Links:

1. Wikipedia.

2. Chemistry LibreTexts.

pressure

pressure inside the system.

Symbol:

p

Latex:

\(p\)

Dimension:

pressure

enthalpy

enthalpy of the system.

Symbol:

H

Latex:

\(H\)

Dimension:

energy

temperature

temperature of the system as a function of pressure and enthalpy.

Symbol:

T(p, H)

Latex:

\(T{\left(p,H \right)}\)

Dimension:

temperature

volume

volume of the system as a function of temperature and pressure.

Symbol:

V(T(p, H), p)

Latex:

\(V{\left(T{\left(p,H \right)},p \right)}\)

Dimension:

volume

isobaric_heat_capacity

heat_capacity of the system at constant pressure.

Symbol:

C_p

Latex:

\(C_{p}\)

Dimension:

energy/temperature

law

Derivative(T(p, H), p) = (T(p, H) * Derivative(V(T(p, H), p), T(p, H)) - V(T(p, H), p)) / C_p

Latex:

\[\frac{\partial}{\partial p} T{\left(p,H \right)} = \frac{T{\left(p,H \right)} \frac{\partial}{\partial T{\left(p,H \right)}} V{\left(T{\left(p,H \right)},p \right)} - V{\left(T{\left(p,H \right)},p \right)}}{C_{p}}\]