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] |
