Changes in Specific Entropy of Ideal Gases with Constant Specific Heats

Changes in specific entropy of ideal gases with constant specific heats

\(\displaystyle s_2-s_1 = s(T_2,v_2)-s(T_1,v_1) = c_v\ln\frac{T_2}{T_1} + R\ln\frac{v_2}{v_1}\)

\(\displaystyle s_2-s_1 = s(T_2,p_2)-s(T_1,p_1) = c_p\ln\frac{T_2}{T_1} - R\ln\frac{p_2}{p_1}\)

\(\displaystyle R = \frac{\bar R}{M}\)

Symbols

\(s\) — specific entropy
\(T\) — thermodynamic temperature
\(v\) — specific volume
\(p\) — absolute pressure
\(R\) — gas constant
\(\bar R\) — universal gas constant, 8314 [J/(kmol·K)]
\(M\) — molar mass
\(c_v\) — constant-volume specific heat
\(c_p\) — constant-pressure specific heat
subscript 1 — state 1
subscript 2 — state 2

Inputs & Outputs

Gas

Select input properties

Initial temperature \(T_1\) [300, 1000] K

Initial specific volume \(v_1\) [0.1, 3] m³/kg

Final temperature \(T_2\) [300, 1000] K

Final specific volume \(v_2\) [0.1, 3] m³/kg

p₁ [kPa]

—

p₂ [kPa]

—

s₂ − s₁ [kJ/(kg·K)]

—

Plots

\(s_2-s_1\) vs \(T_1\)

\(s_2-s_1\) vs \(v_1\)

\(s_2-s_1\) vs \(T_2\)

\(s_2-s_1\) vs \(v_2\)

Each curve varies a single input while holding the other three inputs fixed at their current values. The red dot marks the current state. Use the inputs above to move the red dot, or drag it directly on any plot.