2.7: Key Equations

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Pressure, temperature, and specific volume

Pressure	$0d6114162462a34430e55f5eed91c40d.png$
Absolute and gauge pressures	$P_{gauge}\ =\ P_{abs}\ – P_{atm}$
Absolute and vacuum pressures	$P_{vac}\ =\ P_{atm}\ – P_{abs}$
Density	$6a31f07ad364553cd572c2fb71432d40.png$
Specific volume	$ebe268bed40971368e83e275e4e026e4.png$
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	$bd757755dc57d9decdfd477d62e1d27c.png$
Specific enthalpy	$b6f535a0c11ef2b9dc2d7e8aadeec268.png$ and $h=u+Pv$
Specific entropy	$c0c476971a728d54b61cf2aaf3ecc9d2.png$

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	$s=s_f+x(s_g-s_f)=(1-\ x)s_f+xs_g$