2. Thermodynamic Properties of a Pure Substance

2.6 Key Equations

Pressure, temperature, and specific volume

Pressure [latex]P = F/A[/latex]
Absolute and gauge pressures [latex]P_{gauge}\ =\ P_{abs}\ – P_{atm}[/latex]
Absolute and vacuum pressures [latex]P_{vac}\ =\ P_{atm}\ – P_{abs}[/latex]
Density [latex]\rho=m/\mathbb{V}[/latex]
Specific volume [latex]v=\mathbb{V}/m=1/\rho[/latex]
Conversion of temperatures in Kelvin and Celsius degrees [latex]T\left(\rm{K}\right)=T(^\rm{\circ}C)+273.15[/latex]


Energy, enthalpy, and entropy

Total stored energy in a system [latex]\begin{align*} E &=U+KE+PE\\ &=mu+\dfrac{1}{2}\ mV^2+mgz \; \; \; (V: velocity) \end{align*}[/latex]
Total stored specific energy in a system [latex]e=\displaystyle\frac{E}{m}=u+\frac{1}{2}\ V^2+gz \; \; \; \; (V: velocity)[/latex]
Enthalpy [latex]H=U+P\mathbb{V}[/latex]
Specific internal energy   [latex]u=U/m[/latex]
Specific enthalpy  [latex]h=H/m[/latex]   and   [latex]h=u+Pv[/latex]
Specific entropy  [latex]s=S/m[/latex]


Saturated liquid-vapour two-phase mixtures

Quality [latex]x=\dfrac{m_g}{m_{mix}}[/latex]
Specific volume [latex]v=v_f+x\left(v_g-v_f\right)=\left(1-\ x\right)v_f+xv_g[/latex]
Specific internal energy   [latex]u=u_f+x(u_g-u_f)=(1-\ x)u_f+xu_g[/latex]
Specific enthalpy  [latex]h=h_f+x(h_g-h_f)=(1-\ x)h_f+xh_g[/latex]
Specific entropy  [latex]s=s_f+x(s_g-s_f)=(1-\ x)s_f+xs_g[/latex]


Compressed liquid (when the compressed liquid tables are not available)

Specific volume [latex]v\approx\ v_{f@T}[/latex]
Specific internal energy   [latex]u\approx\ u_{f@T}[/latex]
Specific enthalpy  [latex]h\approx\ h_{f@T}[/latex]
Specific entropy  [latex]s\approx\ s_{f@T}[/latex]


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Introduction to Engineering Thermodynamics Copyright © 2022 by Claire Yu Yan is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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