Change in entropy of ideal gas from volume and temperature

Entropy is a property of a thermodynamic system that expresses the direction or outcome of spontaneous changes in the system. The term was introduced to explain the relationship of the internal energy that is available or unavailable for transformations in form of heat and work. Entropy predicts that certain processes are irreversible or impossible, despite not violating the conservation of energy. The definition of entropy is central to the establishment of the second law of thermodynamics, which states that the entropy of isolated systems cannot decrease with time, as they always tend to arrive at a state of thermodynamic equilibrium, where the entropy is highest.

Notation:

1. \(R\) (R) is molar_gas_constant.

Conditions:

1. The gas is ideal.

Links:

1. Wikipedia.

entropy_change

entropy change during the transition between the two states.

Symbol:

S

Latex:

\(S\)

Dimension:

energy/temperature

mass

mass of the gas.

Symbol:

m

Latex:

\(m\)

Dimension:

mass

molar_mass

molar_mass, or molecular weight, of the gas.

Symbol:

M

Latex:

\(M\)

Dimension:

mass/amount_of_substance

molar_isochoric_heat_capacity

molar_heat_capacity at constant volume.

Symbol:

c_Vm

Latex:

\(c_{V, m}\)

Dimension:

energy/(amount_of_substance*temperature)

final_temperature

temperature of the final state.

Symbol:

T_1

Latex:

\(T_{1}\)

Dimension:

temperature

initial_temperature

temperature of the initial state.

Symbol:

T_0

Latex:

\(T_{0}\)

Dimension:

temperature

final_volume

volume of the final state.

Symbol:

V_1

Latex:

\(V_{1}\)

Dimension:

volume

initial_volume

volume of the initial state.

Symbol:

V_0

Latex:

\(V_{0}\)

Dimension:

volume

law

S = m / M * (c_Vm * log(T_1 / T_0) + R * log(V_1 / V_0))

Latex:

\[S = \frac{m}{M} \left(c_{V, m} \log \left( \frac{T_{1}}{T_{0}} \right) + R \log \left( \frac{V_{1}}{V_{0}} \right)\right)\]