2. Thermodynamic Properties of a Pure Substance

# 2.6 Key Equations

Pressure, temperature, and specific volume

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

Energy, enthalpy, and entropy

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

Saturated liquid-vapour two-phase mixtures

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

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

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